Jika f(x)=x²-2x+2 dan g(x)=x+1,tentukan: a.rumus fungsi (fog)(x) b.nilai a agar (gof) (a)=2

Bab Fungsi Komposisi
Matematika SMA Kelas X

a] (fog) (x) = f(g(x))
                 = f(x + 1)
                 = (x + 1)² - 2(x + 1) + 2
                 = x² + 2x + 1 - 2x - 2 + 2
                 = x² + 1

b] (gof) (a) = 2
    g(f(a)) = 2
    g(a² - 2a + 2) = 2
    a² - 2a + 2 + 1 - 2 = 0
    a² - 2a + 1 = 0
    (a - 1)² = 0
    a - 1 = 0
    a = 1

Fungsi Komposisi.

(f o g)(x) = f(g(x))
= f(x + 1)
= (x + 1)² - 2(x + 1) + 2
= x² + 1

(g o f)(a) = 2
g(f(a)) = 2
g(a² - 2a + 2) = 2
(a + 1)² - 2(a + 1) + 2 = 2
a = 1 ∨ a = -1