Question

Diketahui f: R R dan g : R R didefinisikan dengan (f o g) (x) = x 2 – 2x + 3 dan g(x) = x -6, maka f (x) = ….
A. x 2 – 10x + 27
B. x 2 + 10 x + 27
C. x 2 – 2x + 9
D. x 2 – 14x + 51
E. x 2 – 14x + 49

Sama cara nya ya, biar ngerti hehehe. thanks.

Answer 1

Misal x - 6 = p
maka x = p + 6

fog(x) = x² - 2x + 3
f(g(x)) = x² - 2x + 3
f(x - 6)= x² - 2x + 3
f(p)     = (p + 6)² - 2(p + 6) + 3
f(p)     = p² + 12p + 36 -2p - 12 + 3
f(p)     = p² +10p + 27
f(x)     = x² +10x + 27

Answer 2

(f o g)(x)= x²-2x+3
g(x)= x-6
f(x)= ...?

(f o g)(x)= x²-2x+3
f (g(x)) = x²-2x+3
f (x-6) = x²-2x+3

⇒misal, x-6= p, maka x= p-6
f(p) = p² - 2p + 3
f(p) = (p+6)² - 2(p+6) + 3
f(p) = p²+12p+36 - 2p-12 +3
f(p) = p² + 10p + 27
⇒jadi f(x)= x²+10x+27 (B)