{"id":2123,"date":"2026-04-03T14:08:43","date_gmt":"2026-04-03T14:08:43","guid":{"rendered":"https:\/\/rumahpintar.co.id\/blog\/?p=2123"},"modified":"2026-04-08T19:16:36","modified_gmt":"2026-04-08T19:16:36","slug":"15-contoh-soal-relasi-dan-fungsi","status":"publish","type":"post","link":"https:\/\/rumahpintar.co.id\/blog\/15-contoh-soal-relasi-dan-fungsi\/","title":{"rendered":"15 Contoh Soal Relasi dan Fungsi (Domain, Kodomain, Range) dan Pembahasannya"},"content":{"rendered":"

Bimbel Rumah Pintar<\/a> – Sahabat Rumah Pintar<\/strong>, relasi dan fungsi (pemetaan) adalah konsep matematika yang menghubungkan dua himpunan, dengan fungsi sebagai relasi khusus di mana setiap anggota domain dipasangkan dengan tepat satu anggota kodomain.<\/p>\n

Prinsip dasar yang harus dipegang teguh adalah:\u00a0setiap anggota domain (daerah asal) harus memiliki pasangan, dan pasangannya hanya satu di kodomain (daerah kawan)<\/strong>.<\/p>\n

Tiga istilah kunci yang wajib dikuasai adalah\u00a0domain<\/strong>\u00a0(himpunan semua nilai input\u00a0x<\/span>x<\/span><\/span><\/span><\/span>),\u00a0kodomain<\/strong>\u00a0(himpunan semua nilai output yang mungkin), dan\u00a0range<\/strong>\u00a0(himpunan nilai output yang benar-benar dihasilkan). Penyajian fungsi dapat dilakukan dalam bentuk diagram panah, diagram Cartesius (grafik), himpunan pasangan berurutan, atau rumus fungsi\u00a0f(x)=ax+b<\/span>f<\/span>(<\/span>x<\/span>)<\/span>=<\/span><\/span>a<\/span>x<\/span>+<\/span><\/span>b<\/span><\/span><\/span><\/span>.<\/p>\n

Tanpa latihan yang cukup, siswa sering keliru dalam menghitung nilai fungsi (lupa mengalikan koefisien), tertukar antara domain dan range, atau salah menentukan domain fungsi rasional dan akar. Dengan menguasai 15 variasi soal berikut, Sahabat Rumah Pintar akan mampu mengidentifikasi fungsi, menghitung nilai fungsi dengan tepat, dan menjawab soal TKA dengan percaya diri.<\/p>\n

15 Contoh Soal Relasi dan Fungsi dan Pembahasannya<\/h2>\n
\n

Soal 1 (Nilai Fungsi dari Rumus)<\/h3>\n

Fungsi\u00a0f(x)=5x+10<\/span>f<\/span>(<\/span>x<\/span>)<\/span>=<\/span><\/span>5<\/span>x<\/span>+<\/span><\/span>10<\/span><\/span><\/span><\/span>\u00a0menyatakan berat total (kg) untuk\u00a0x<\/span>x<\/span><\/span><\/span><\/span>\u00a0batang logam. Jika pabrik memproduksi 7 batang logam, berapa total berat logam yang dihasilkan?<\/p>\n

Pembahasan:<\/strong><\/p>\n

    \n
  • \n

    Substitusi\u00a0x=7<\/span>x<\/span>=<\/span><\/span>7<\/span><\/span><\/span><\/span>\u00a0ke\u00a0f(x)=5x+10<\/span>f<\/span>(<\/span>x<\/span>)<\/span>=<\/span><\/span>5<\/span>x<\/span>+<\/span><\/span>10<\/span><\/span><\/span><\/span><\/p>\n<\/li>\n

  • \n

    f(7)=5(7)+10=35+10=45<\/span>f<\/span>(<\/span>7<\/span>)<\/span>=<\/span><\/span>5<\/span>(<\/span>7<\/span>)<\/span>+<\/span><\/span>10<\/span>=<\/span><\/span>35<\/span>+<\/span><\/span>10<\/span>=<\/span><\/span>45<\/span><\/span><\/span><\/span><\/p>\n<\/li>\n<\/ul>\n

    Jawaban: 45 kg<\/strong><\/p>\n

    \n

    Soal 2 (Menentukan Rumus Fungsi dari Dua Titik)<\/h3>\n

    Diketahui fungsi\u00a0f(x)=ax+b<\/span>f<\/span>(<\/span>x<\/span>)<\/span>=<\/span><\/span>a<\/span>x<\/span>+<\/span><\/span>b<\/span><\/span><\/span><\/span>. Jika\u00a0f(3)=14<\/span>f<\/span>(<\/span>3<\/span>)<\/span>=<\/span><\/span>14<\/span><\/span><\/span><\/span>\u00a0dan\u00a0f(5)=22<\/span>f<\/span>(<\/span>5<\/span>)<\/span>=<\/span><\/span>22<\/span><\/span><\/span><\/span>, tentukan rumus fungsi\u00a0f(x)<\/span>f<\/span>(<\/span>x<\/span>)<\/span><\/span><\/span><\/span>.<\/p>\n

    Pembahasan:<\/strong><\/p>\n

      \n
    • \n

      f(3)=3a+b=14<\/span>f<\/span>(<\/span>3<\/span>)<\/span>=<\/span><\/span>3<\/span>a<\/span>+<\/span><\/span>b<\/span>=<\/span><\/span>14<\/span><\/span><\/span><\/span><\/p>\n<\/li>\n

    • \n

      f(5)=5a+b=22<\/span>f<\/span>(<\/span>5<\/span>)<\/span>=<\/span><\/span>5<\/span>a<\/span>+<\/span><\/span>b<\/span>=<\/span><\/span>22<\/span><\/span><\/span><\/span><\/p>\n<\/li>\n

    • \n

      Eliminasi:\u00a0(5a+b)\u2212(3a+b)=22\u221214\u21922a=8\u2192a=4<\/span>(<\/span>5<\/span>a<\/span>+<\/span><\/span>b<\/span>)<\/span>\u2212<\/span><\/span>(<\/span>3<\/span>a<\/span>+<\/span><\/span>b<\/span>)<\/span>=<\/span><\/span>22<\/span>\u2212<\/span><\/span>14<\/span>\u2192<\/span><\/span>2<\/span>a<\/span>=<\/span><\/span>8<\/span>\u2192<\/span><\/span>a<\/span>=<\/span><\/span>4<\/span><\/span><\/span><\/span><\/p>\n<\/li>\n

    • \n

      Substitusi\u00a0a=4<\/span>a<\/span>=<\/span><\/span>4<\/span><\/span><\/span><\/span>\u00a0ke\u00a03a+b=14\u219212+b=14\u2192b=2<\/span>3<\/span>a<\/span>+<\/span><\/span>b<\/span>=<\/span><\/span>14<\/span>\u2192<\/span><\/span>12<\/span>+<\/span><\/span>b<\/span>=<\/span><\/span>14<\/span>\u2192<\/span><\/span>b<\/span>=<\/span><\/span>2<\/span><\/span><\/span><\/span><\/p>\n<\/li>\n

    • \n

      f(x)=4x+2<\/span>f<\/span>(<\/span>x<\/span>)<\/span>=<\/span><\/span>4<\/span>x<\/span>+<\/span><\/span>2<\/span><\/span><\/span><\/span><\/p>\n<\/li>\n<\/ul>\n

      Jawaban:\u00a0f(x)=4x+2<\/span>f<\/span>(<\/span>x<\/span>)<\/span>=<\/span><\/span>4<\/span>x<\/span>+<\/span><\/span>2<\/span><\/span><\/span><\/span><\/strong><\/p>\n

      \n

      Soal 3 (Menentukan Nilai Fungsi Kuadrat)<\/h3>\n

      Jika\u00a0f(x)=3×2\u22122x+1<\/span>f<\/span>(<\/span>x<\/span>)<\/span>=<\/span><\/span>3<\/span>x<\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span>2<\/span>x<\/span>+<\/span><\/span>1<\/span><\/span><\/span><\/span>, tentukan\u00a0f(\u22122)<\/span>f<\/span>(<\/span>\u2212<\/span>2<\/span>)<\/span><\/span><\/span><\/span>.<\/p>\n

      Pembahasan:<\/strong><\/p>\n

        \n
      • \n

        f(\u22122)=3(\u22122)2\u22122(\u22122)+1<\/span>f<\/span>(<\/span>\u2212<\/span>2<\/span>)<\/span>=<\/span><\/span>3<\/span>(<\/span>\u2212<\/span>2<\/span>)2<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span>2<\/span>(<\/span>\u2212<\/span>2<\/span>)<\/span>+<\/span><\/span>1<\/span><\/span><\/span><\/span><\/p>\n<\/li>\n

      • \n

        =3(4)+4+1<\/span>=<\/span><\/span>3<\/span>(<\/span>4<\/span>)<\/span>+<\/span><\/span>4<\/span>+<\/span><\/span>1<\/span><\/span><\/span><\/span><\/p>\n<\/li>\n

      • \n

        =12+4+1=17<\/span>=<\/span><\/span>12<\/span>+<\/span><\/span>4<\/span>+<\/span><\/span>1<\/span>=<\/span><\/span>17<\/span><\/span><\/span><\/span><\/p>\n<\/li>\n<\/ul>\n

        Jawaban: 17<\/strong><\/p>\n

        \n

        Soal 4 (Domain dan Range Fungsi Linear dengan Domain Tertentu)<\/h3>\n

        Fungsi\u00a0f(x)=2x+3<\/span>f<\/span>(<\/span>x<\/span>)<\/span>=<\/span><\/span>2<\/span>x<\/span>+<\/span><\/span>3<\/span><\/span><\/span><\/span>\u00a0dengan domain\u00a0{1,2,3,4}<\/span>{<\/span>1<\/span>,<\/span>2<\/span>,<\/span>3<\/span>,<\/span>4<\/span>}<\/span><\/span><\/span><\/span>. Tentukan range-nya.<\/p>\n

        Pembahasan:<\/strong><\/p>\n

          \n
        • \n

          f(1)=2(1)+3=5<\/span>f<\/span>(<\/span>1<\/span>)<\/span>=<\/span><\/span>2<\/span>(<\/span>1<\/span>)<\/span>+<\/span><\/span>3<\/span>=<\/span><\/span>5<\/span><\/span><\/span><\/span><\/p>\n<\/li>\n

        • \n

          f(2)=2(2)+3=7<\/span>f<\/span>(<\/span>2<\/span>)<\/span>=<\/span><\/span>2<\/span>(<\/span>2<\/span>)<\/span>+<\/span><\/span>3<\/span>=<\/span><\/span>7<\/span><\/span><\/span><\/span><\/p>\n<\/li>\n

        • \n

          f(3)=2(3)+3=9<\/span>f<\/span>(<\/span>3<\/span>)<\/span>=<\/span><\/span>2<\/span>(<\/span>3<\/span>)<\/span>+<\/span><\/span>3<\/span>=<\/span><\/span>9<\/span><\/span><\/span><\/span><\/p>\n<\/li>\n

        • \n

          f(4)=2(4)+3=11<\/span>f<\/span>(<\/span>4<\/span>)<\/span>=<\/span><\/span>2<\/span>(<\/span>4<\/span>)<\/span>+<\/span><\/span>3<\/span>=<\/span><\/span>11<\/span><\/span><\/span><\/span><\/p>\n<\/li>\n<\/ul>\n

          Jawaban: Range =\u00a0{5,7,9,11}<\/span>{<\/span>5<\/span>,<\/span>7<\/span>,<\/span>9<\/span>,<\/span>11<\/span>}<\/span><\/span><\/span><\/span><\/strong><\/p>\n

          \n

          Soal 5 (Mengidentifikasi Fungsi dari Diagram Panah)<\/h3>\n

          Perhatikan diagram panah berikut: A = {1, 2, 3} \u2192 B = {2, 4, 6, 8} dengan pemetaan 1 \u2192 2, 2 \u2192 4, 3 \u2192 6. Apakah ini fungsi? Tentukan domain, kodomain, dan range.<\/p>\n

          Pembahasan:<\/strong><\/p>\n

            \n
          • \n

            Setiap anggota A punya tepat satu pasangan di B \u2192\u00a0merupakan fungsi<\/strong><\/p>\n<\/li>\n

          • \n

            Domain = {1, 2, 3}<\/p>\n<\/li>\n

          • \n

            Kodomain = {2, 4, 6, 8}<\/p>\n<\/li>\n

          • \n

            Range = {2, 4, 6}<\/p>\n<\/li>\n<\/ul>\n

            Jawaban: Fungsi, domain = {1,2,3}, kodomain = {2,4,6,8}, range = {2,4,6}<\/strong><\/p>\n

            \n

            Soal 6 (Fungsi dalam Himpunan Pasangan Berurutan)<\/h3>\n

            Manakah yang merupakan fungsi? Berikan alasan.
            \nA. {(1,2), (2,3), (2,4), (3,5)}
            \nB. {(1,2), (2,3), (3,4), (4,5)}<\/p>\n

            Pembahasan:<\/strong><\/p>\n

              \n
            • \n

              A: Anggota domain 2 memiliki dua pasangan (3 dan 4) \u2192\u00a0bukan fungsi<\/strong><\/p>\n<\/li>\n

            • \n

              B: Setiap anggota domain (1,2,3,4) punya tepat satu pasangan \u2192\u00a0fungsi<\/strong><\/p>\n<\/li>\n<\/ul>\n

              Jawaban: B adalah fungsi<\/strong><\/p>\n

              \n

              Soal 7 (Soal Cerita \u2013 Fungsi Biaya Taksi)<\/h3>\n

              Sebuah taksi mengenakan tarif Rp7.000 untuk 1 km pertama dan Rp3.500 per km berikutnya. Buatlah fungsi biaya\u00a0f(x)<\/span>f<\/span>(<\/span>x<\/span>)<\/span><\/span><\/span><\/span>\u00a0untuk\u00a0x<\/span>x<\/span><\/span><\/span><\/span>\u00a0km dengan\u00a0x\u22651<\/span>x<\/span>\u2265<\/span><\/span>1<\/span><\/span><\/span><\/span>.<\/p>\n

              Pembahasan:<\/strong><\/p>\n

                \n
              • \n

                Untuk 1 km pertama: Rp7.000<\/p>\n<\/li>\n

              • \n

                Untuk km berikutnya\u00a0(x\u22121)<\/span>(<\/span>x<\/span>\u2212<\/span><\/span>1<\/span>)<\/span><\/span><\/span><\/span>\u00a0km: Rp3.500 \u00d7\u00a0(x\u22121)<\/span>(<\/span>x<\/span>\u2212<\/span><\/span>1<\/span>)<\/span><\/span><\/span><\/span><\/p>\n<\/li>\n

              • \n

                f(x)=7.000+3.500(x\u22121)<\/span>f<\/span>(<\/span>x<\/span>)<\/span>=<\/span><\/span>7.000<\/span>+<\/span><\/span>3.500<\/span>(<\/span>x<\/span>\u2212<\/span><\/span>1<\/span>)<\/span><\/span><\/span><\/span><\/p>\n<\/li>\n

              • \n

                f(x)=7.000+3.500x\u22123.500<\/span>f<\/span>(<\/span>x<\/span>)<\/span>=<\/span><\/span>7.000<\/span>+<\/span><\/span>3.500<\/span>x<\/span>\u2212<\/span><\/span>3.500<\/span><\/span><\/span><\/span><\/p>\n<\/li>\n

              • \n

                f(x)=3.500x+3.500<\/span>f<\/span>(<\/span>x<\/span>)<\/span>=<\/span><\/span>3.500<\/span>x<\/span>+<\/span><\/span>3.500<\/span><\/span><\/span><\/span><\/p>\n<\/li>\n<\/ul>\n

                Jawaban:\u00a0f(x)=3.500x+3.500<\/span>f<\/span>(<\/span>x<\/span>)<\/span>=<\/span><\/span>3.500<\/span>x<\/span>+<\/span><\/span>3.500<\/span><\/span><\/span><\/span><\/strong><\/p>\n

                \n

                Soal 8 (Menentukan Nilai x jika f(x) Diketahui)<\/h3>\n

                Jika\u00a0f(x)=4x\u22127<\/span>f<\/span>(<\/span>x<\/span>)<\/span>=<\/span><\/span>4<\/span>x<\/span>\u2212<\/span><\/span>7<\/span><\/span><\/span><\/span>\u00a0dan\u00a0f(x)=13<\/span>f<\/span>(<\/span>x<\/span>)<\/span>=<\/span><\/span>13<\/span><\/span><\/span><\/span>, tentukan nilai\u00a0x<\/span>x<\/span><\/span><\/span><\/span>.<\/p>\n

                Pembahasan:<\/strong><\/p>\n

                  \n
                • \n

                  4x\u22127=13<\/span>4<\/span>x<\/span>\u2212<\/span><\/span>7<\/span>=<\/span><\/span>13<\/span><\/span><\/span><\/span><\/p>\n<\/li>\n

                • \n

                  4x=20<\/span>4<\/span>x<\/span>=<\/span><\/span>20<\/span><\/span><\/span><\/span><\/p>\n<\/li>\n

                • \n

                  x=5<\/span>x<\/span>=<\/span><\/span>5<\/span><\/span><\/span><\/span><\/p>\n<\/li>\n<\/ul>\n

                  Jawaban:\u00a0x=5<\/span>x<\/span>=<\/span><\/span>5<\/span><\/span><\/span><\/span><\/strong><\/p>\n

                  \n

                  Soal 9 (Fungsi Konstan)<\/h3>\n

                  Diketahui\u00a0f(x)=8<\/span>f<\/span>(<\/span>x<\/span>)<\/span>=<\/span><\/span>8<\/span><\/span><\/span><\/span>. Tentukan\u00a0f(2)+f(5)<\/span>f<\/span>(<\/span>2<\/span>)<\/span>+<\/span><\/span>f<\/span>(<\/span>5<\/span>)<\/span><\/span><\/span><\/span>.<\/p>\n

                  Pembahasan:<\/strong><\/p>\n

                    \n
                  • \n

                    Fungsi konstan \u2192 berapapun\u00a0x<\/span>x<\/span><\/span><\/span><\/span>,\u00a0f(x)=8<\/span>f<\/span>(<\/span>x<\/span>)<\/span>=<\/span><\/span>8<\/span><\/span><\/span><\/span><\/p>\n<\/li>\n

                  • \n

                    f(2)=8<\/span>f<\/span>(<\/span>2<\/span>)<\/span>=<\/span><\/span>8<\/span><\/span><\/span><\/span>,\u00a0f(5)=8<\/span>f<\/span>(<\/span>5<\/span>)<\/span>=<\/span><\/span>8<\/span><\/span><\/span><\/span><\/p>\n<\/li>\n

                  • \n

                    f(2)+f(5)=8+8=16<\/span>f<\/span>(<\/span>2<\/span>)<\/span>+<\/span><\/span>f<\/span>(<\/span>5<\/span>)<\/span>=<\/span><\/span>8<\/span>+<\/span><\/span>8<\/span>=<\/span><\/span>16<\/span><\/span><\/span><\/span><\/p>\n<\/li>\n<\/ul>\n

                    Jawaban: 16<\/strong><\/p>\n

                    \n

                    Soal 10 (Menentukan Rumus Fungsi dari Tabel)<\/h3>\n

                    Dari tabel berikut, tentukan rumus fungsi\u00a0f(x)<\/span>f<\/span>(<\/span>x<\/span>)<\/span><\/span><\/span><\/span>.<\/p>\n

                    \n
                    \n
                    <\/div>\n
                    <\/div>\n<\/div>\n\n\n\n\n\n
                    x<\/span>x<\/span><\/span><\/span><\/span><\/th>\n1<\/th>\n2<\/th>\n3<\/th>\n4<\/th>\n<\/tr>\n<\/thead>\n
                    f(x)<\/span>f<\/span>(<\/span>x<\/span>)<\/span><\/span><\/span><\/span><\/td>\n6<\/td>\n9<\/td>\n12<\/td>\n15<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n

                    Pembahasan:<\/strong><\/p>\n

                      \n
                    • \n

                      Selisih\u00a0f(x)<\/span>f<\/span>(<\/span>x<\/span>)<\/span><\/span><\/span><\/span>\u00a0= 3 untuk setiap kenaikan\u00a0x=1<\/span>x<\/span>=<\/span><\/span>1<\/span><\/span><\/span><\/span>\u00a0\u2192\u00a0a=3<\/span>a<\/span>=<\/span><\/span>3<\/span><\/span><\/span><\/span><\/p>\n<\/li>\n

                    • \n

                      f(x)=3x+b<\/span>f<\/span>(<\/span>x<\/span>)<\/span>=<\/span><\/span>3<\/span>x<\/span>+<\/span><\/span>b<\/span><\/span><\/span><\/span><\/p>\n<\/li>\n

                    • \n

                      Substitusi\u00a0x=1<\/span>x<\/span>=<\/span><\/span>1<\/span><\/span><\/span><\/span>,\u00a0f(1)=6<\/span>f<\/span>(<\/span>1<\/span>)<\/span>=<\/span><\/span>6<\/span><\/span><\/span><\/span>:\u00a03(1)+b=6\u21923+b=6\u2192b=3<\/span>3<\/span>(<\/span>1<\/span>)<\/span>+<\/span><\/span>b<\/span>=<\/span><\/span>6<\/span>\u2192<\/span><\/span>3<\/span>+<\/span><\/span>b<\/span>=<\/span><\/span>6<\/span>\u2192<\/span><\/span>b<\/span>=<\/span><\/span>3<\/span><\/span><\/span><\/span><\/p>\n<\/li>\n

                    • \n

                      f(x)=3x+3<\/span>f<\/span>(<\/span>x<\/span>)<\/span>=<\/span><\/span>3<\/span>x<\/span>+<\/span><\/span>3<\/span><\/span><\/span><\/span><\/p>\n<\/li>\n<\/ul>\n

                      Jawaban:\u00a0f(x)=3x+3<\/span>f<\/span>(<\/span>x<\/span>)<\/span>=<\/span><\/span>3<\/span>x<\/span>+<\/span><\/span>3<\/span><\/span><\/span><\/span><\/strong><\/p>\n

                      \n

                      Soal 11 (Domain Fungsi Rasional)<\/h3>\n

                      Tentukan domain dari fungsi\u00a0f(x)=2x\u22123<\/span>f<\/span>(<\/span>x<\/span>)<\/span>=<\/span><\/span>x<\/span>\u2212<\/span>3<\/span><\/span>2<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>.<\/p>\n

                      Pembahasan:<\/strong><\/p>\n

                        \n
                      • \n

                        Fungsi rasional tidak terdefinisi jika penyebut = 0<\/p>\n<\/li>\n

                      • \n

                        x\u22123\u22600\u2192x\u22603<\/span>x<\/span>\u2212<\/span><\/span>3<\/span>\ue020<\/span><\/span><\/span><\/span><\/span>=<\/span><\/span>0<\/span>\u2192<\/span><\/span>x<\/span>\ue020<\/span><\/span><\/span><\/span><\/span>=<\/span><\/span>3<\/span><\/span><\/span><\/span><\/p>\n<\/li>\n

                      • \n

                        Domain = semua bilangan real kecuali 3<\/p>\n<\/li>\n<\/ul>\n

                        Jawaban:\u00a0{x\u2223x\u22603,x\u2208R}<\/span>{<\/span>x<\/span>\u2223<\/span><\/span>x<\/span>\ue020<\/span><\/span><\/span><\/span><\/span>=<\/span><\/span>3<\/span>,<\/span>x<\/span>\u2208<\/span><\/span>R<\/span>}<\/span><\/span><\/span><\/span><\/strong><\/p>\n

                        \n

                        Soal 12 (Domain Fungsi Akar)<\/h3>\n

                        Tentukan domain dari fungsi\u00a0f(x)=x\u22124<\/span>f<\/span>(<\/span>x<\/span>)<\/span>=<\/span><\/span>x<\/span>\u2212<\/span>4<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span>.<\/p>\n

                        Pembahasan:<\/strong><\/p>\n

                          \n
                        • \n

                          Fungsi akar terdefinisi jika dalam akar\u00a0\u22650<\/span>\u2265<\/span><\/span>0<\/span><\/span><\/span><\/span><\/p>\n<\/li>\n

                        • \n

                          x\u22124\u22650\u2192x\u22654<\/span>x<\/span>\u2212<\/span><\/span>4<\/span>\u2265<\/span><\/span>0<\/span>\u2192<\/span><\/span>x<\/span>\u2265<\/span><\/span>4<\/span><\/span><\/span><\/span><\/p>\n<\/li>\n<\/ul>\n

                          Jawaban:\u00a0{x\u2223x\u22654,x\u2208R}<\/span>{<\/span>x<\/span>\u2223<\/span><\/span>x<\/span>\u2265<\/span><\/span>4<\/span>,<\/span>x<\/span>\u2208<\/span><\/span>R<\/span>}<\/span><\/span><\/span><\/span><\/strong><\/p>\n

                          \n

                          Soal 13 (Fungsi Linear dari Soal Cerita Produksi)<\/h3>\n

                          Sebuah perusahaan memproduksi barang dengan biaya tetap Rp200.000 dan biaya variabel Rp15.000 per unit. Buatlah fungsi biaya total\u00a0f(x)<\/span>f<\/span>(<\/span>x<\/span>)<\/span><\/span><\/span><\/span>\u00a0untuk\u00a0x<\/span>x<\/span><\/span><\/span><\/span>\u00a0unit barang.<\/p>\n

                          Pembahasan:<\/strong><\/p>\n

                            \n
                          • \n

                            Biaya tetap = Rp200.000<\/p>\n<\/li>\n

                          • \n

                            Biaya variabel = Rp15.000 \u00d7\u00a0x<\/span>x<\/span><\/span><\/span><\/span><\/p>\n<\/li>\n

                          • \n

                            f(x)=15.000x+200.000<\/span>f<\/span>(<\/span>x<\/span>)<\/span>=<\/span><\/span>15.000<\/span>x<\/span>+<\/span><\/span>200.000<\/span><\/span><\/span><\/span><\/p>\n<\/li>\n<\/ul>\n

                            Jawaban:\u00a0f(x)=15.000x+200.000<\/span>f<\/span>(<\/span>x<\/span>)<\/span>=<\/span><\/span>15.000<\/span>x<\/span>+<\/span><\/span>200.000<\/span><\/span><\/span><\/span><\/strong><\/p>\n

                            \n

                            Soal 14 (Operasi Dua Fungsi)<\/h3>\n

                            Diketahui fungsi\u00a0f(x)=4x+1<\/span>f<\/span>(<\/span>x<\/span>)<\/span>=<\/span><\/span>4<\/span>x<\/span>+<\/span><\/span>1<\/span><\/span><\/span><\/span>\u00a0dan\u00a0g(x)=2x\u22123<\/span>g<\/span>(<\/span>x<\/span>)<\/span>=<\/span><\/span>2<\/span>x<\/span>\u2212<\/span><\/span>3<\/span><\/span><\/span><\/span>. Tentukan\u00a0f(2)+g(3)<\/span>f<\/span>(<\/span>2<\/span>)<\/span>+<\/span><\/span>g<\/span>(<\/span>3<\/span>)<\/span><\/span><\/span><\/span>.<\/p>\n

                            Pembahasan:<\/strong><\/p>\n

                              \n
                            • \n

                              f(2)=4(2)+1=8+1=9<\/span>f<\/span>(<\/span>2<\/span>)<\/span>=<\/span><\/span>4<\/span>(<\/span>2<\/span>)<\/span>+<\/span><\/span>1<\/span>=<\/span><\/span>8<\/span>+<\/span><\/span>1<\/span>=<\/span><\/span>9<\/span><\/span><\/span><\/span><\/p>\n<\/li>\n

                            • \n

                              g(3)=2(3)\u22123=6\u22123=3<\/span>g<\/span>(<\/span>3<\/span>)<\/span>=<\/span><\/span>2<\/span>(<\/span>3<\/span>)<\/span>\u2212<\/span><\/span>3<\/span>=<\/span><\/span>6<\/span>\u2212<\/span><\/span>3<\/span>=<\/span><\/span>3<\/span><\/span><\/span><\/span><\/p>\n<\/li>\n

                            • \n

                              f(2)+g(3)=9+3=12<\/span>f<\/span>(<\/span>2<\/span>)<\/span>+<\/span><\/span>g<\/span>(<\/span>3<\/span>)<\/span>=<\/span><\/span>9<\/span>+<\/span><\/span>3<\/span>=<\/span><\/span>12<\/span><\/span><\/span><\/span><\/p>\n<\/li>\n<\/ul>\n

                              Jawaban: 12<\/strong><\/p>\n

                              \n

                              Soal 15 (Menentukan Nilai a dari Fungsi)<\/h3>\n

                              Jika\u00a0f(x)=5x+8<\/span>f<\/span>(<\/span>x<\/span>)<\/span>=<\/span><\/span>5<\/span>x<\/span>+<\/span><\/span>8<\/span><\/span><\/span><\/span>\u00a0dan\u00a0f(a)=33<\/span>f<\/span>(<\/span>a<\/span>)<\/span>=<\/span><\/span>33<\/span><\/span><\/span><\/span>, tentukan nilai\u00a0a<\/span>a<\/span><\/span><\/span><\/span>.<\/p>\n

                              Pembahasan:<\/strong><\/p>\n

                                \n
                              • \n

                                5a+8=33<\/span>5<\/span>a<\/span>+<\/span><\/span>8<\/span>=<\/span><\/span>33<\/span><\/span><\/span><\/span><\/p>\n<\/li>\n

                              • \n

                                5a=25<\/span>5<\/span>a<\/span>=<\/span><\/span>25<\/span><\/span><\/span><\/span><\/p>\n<\/li>\n

                              • \n

                                a=5<\/span>a<\/span>=<\/span><\/span>5<\/span><\/span><\/span><\/span><\/p>\n<\/li>\n<\/ul>\n

                                Jawaban:\u00a0a=5<\/span>a<\/span>=<\/span><\/span>5<\/span><\/span><\/span><\/span><\/strong><\/p>\n

                                \n

                                Ringkasan Materi Relasi dan Fungsi<\/h2>\n
                                \n
                                \n
                                <\/div>\n
                                <\/div>\n<\/div>\n\n\n\n\n\n\n\n\n\n
                                Konsep<\/th>\nPenjelasan<\/th>\nContoh<\/th>\n<\/tr>\n<\/thead>\n
                                Relasi<\/strong><\/td>\nHubungan antara dua himpunan<\/td>\n1 \u2192 2, 2 \u2192 4, 3 \u2192 6<\/td>\n<\/tr>\n
                                Fungsi<\/strong><\/td>\nRelasi khusus: setiap domain punya tepat satu pasangan<\/td>\nf(x)=2x+3<\/span>f<\/span>(<\/span>x<\/span>)<\/span>=<\/span><\/span>2<\/span>x<\/span>+<\/span><\/span>3<\/span><\/span><\/span><\/span><\/td>\n<\/tr>\n
                                Domain<\/strong><\/td>\nHimpunan semua nilai input (x<\/span>x<\/span><\/span><\/span><\/span>)<\/td>\n{1, 2, 3, 4}<\/td>\n<\/tr>\n
                                Kodomain<\/strong><\/td>\nHimpunan semua nilai output yang mungkin<\/td>\n{2, 4, 6, 8}<\/td>\n<\/tr>\n
                                Range<\/strong><\/td>\nHimpunan nilai output yang benar-benar dihasilkan<\/td>\n{5, 7, 9, 11}<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n

                                Aturan Penting:<\/strong><\/p>\n

                                  \n
                                • \n

                                  Fungsi linear:\u00a0f(x)=ax+b<\/span>f<\/span>(<\/span>x<\/span>)<\/span>=<\/span><\/span>a<\/span>x<\/span>+<\/span><\/span>b<\/span><\/span><\/span><\/span><\/p>\n<\/li>\n

                                • \n

                                  Fungsi konstan:\u00a0f(x)=c<\/span>f<\/span>(<\/span>x<\/span>)<\/span>=<\/span><\/span>c<\/span><\/span><\/span><\/span><\/p>\n<\/li>\n

                                • \n

                                  Domain fungsi rasional: penyebut\u00a0\u22600<\/span>\ue020<\/span><\/span><\/span><\/span><\/span>=<\/span><\/span>0<\/span><\/span><\/span><\/span><\/p>\n<\/li>\n

                                • \n

                                  Domain fungsi akar: dalam akar\u00a0\u22650<\/span>\u2265<\/span><\/span>0<\/span><\/span><\/span><\/span><\/p>\n<\/li>\n<\/ul>\n

                                  \n

                                  Sahabat Rumah Pintar<\/strong>, dengan menguasai 15 soal di atas, kalian sudah siap membedakan relasi dan fungsi, menentukan domain, kodomain, dan range, menghitung nilai fungsi, serta menyelesaikan soal cerita fungsi di TKA Matematika SMP. Ingat kuncinya:\u00a0setiap anggota domain harus dipasangkan dengan tepat satu anggota kodomain<\/strong>.<\/p>\n","protected":false},"excerpt":{"rendered":"

                                  Bimbel Rumah Pintar – Sahabat Rumah Pintar, relasi dan fungsi (pemetaan) adalah konsep matematika yang menghubungkan dua himpunan, dengan fungsi sebagai relasi khusus di mana setiap anggota domain dipasangkan dengan tepat satu anggota kodomain. Prinsip dasar yang harus dipegang teguh […]<\/p>\n","protected":false},"author":1,"featured_media":2125,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"default","adv-header-id-meta":"","stick-header-meta":"default","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"set","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[4],"tags":[224],"class_list":["post-2123","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-bahas-soal","tag-soal-tka-matematika-smp"],"_links":{"self":[{"href":"https:\/\/rumahpintar.co.id\/blog\/wp-json\/wp\/v2\/posts\/2123","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/rumahpintar.co.id\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/rumahpintar.co.id\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/rumahpintar.co.id\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/rumahpintar.co.id\/blog\/wp-json\/wp\/v2\/comments?post=2123"}],"version-history":[{"count":1,"href":"https:\/\/rumahpintar.co.id\/blog\/wp-json\/wp\/v2\/posts\/2123\/revisions"}],"predecessor-version":[{"id":2127,"href":"https:\/\/rumahpintar.co.id\/blog\/wp-json\/wp\/v2\/posts\/2123\/revisions\/2127"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/rumahpintar.co.id\/blog\/wp-json\/wp\/v2\/media\/2125"}],"wp:attachment":[{"href":"https:\/\/rumahpintar.co.id\/blog\/wp-json\/wp\/v2\/media?parent=2123"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/rumahpintar.co.id\/blog\/wp-json\/wp\/v2\/categories?post=2123"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/rumahpintar.co.id\/blog\/wp-json\/wp\/v2\/tags?post=2123"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}