Matematika

Pertanyaan

diketahui fungsi f(x)=4-2x dan g(x) =2x^2-4 . tebtukanlah komposisi berikut ! a. (fog)(x) , b(gof)(x) , (fog)(1, dan (gof)(2)

1 Jawaban

  • f(x) = 4-2x
    g(x) = 2x²-4

    a) (fog)(x) = f(g(x)) = 4-2(g(x))
    = 4-2(2x²-4)
    = 4 -4x² + 8
    = -4x² + 12

    b) (gof)(x) = g(f(x)) = 2(f(x))²-4 = 2(4-2x)²-4
    = 2 (16-16x+4x²) - 4
    = 32-32x+8x²-4
    = 8x² -32x + 32 -4
    = 8x² -32x + 28

    c) (fog)(1) = -4x² + 12 = -4(1)² + 12 = 8

    d) (gof)(2) = 8x² -32x + 28 = 8(2)² -32(2) + 28
    = 32 - 64 + 28 = -4

    semoga membantuu, dikoreksi lagi yaa

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