Diketahui f(x) = 2x + 1, g(x) = 5 – 3x, dan h(x) = x2 – 1 Tentukan: a. (fog)(x) =

Diketahui f(x) = 2x + 1, g(x) = 5 – 3x, dan h(x) = x² – 1

Tentukan:

    a. (fog)(x) =

    b. (gof)(x) =

    c. (fogoh)(x) =

    d. (fog)(-2) =

    e. (gofoh)(3) =

Jawab:

a. (fog)(x) = 2(5 – 3x) + 1 = 11 – 6x

b. (gof)(x) = 5 – 3(2x + 1) = 2 – 6x

c. (goh)(x) = 5 – 3(x² – 1) = 8 – 3x²

    (fogoh)(x) = 2(8 – 3x²) + 1 = 17 – 6x²

d. (fog)(-2) = 11 – 6(-2) = 11 + 12 = 23

e. h(3) = 3² – 1 = 8

    (foh)(3) = f(8) = 2 . 8 + 1 = 17

    (gofoh)(3) = g(17) = 5 – 3(17) = -46

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