Question

Diketahui (f ° g) (x) = 4x^2 + 8x - 3 dan g(x) = 2x + 4. Nilai f(-2)=?

Answer 1

(f ° g) (x) = 4x^2 + 8x - 3 dan g(x) = 2x + 4. Nilai f(-2)


(f ° g) (x) = 4x² + 8x - 3
f(g(x)) = 4x² + 8x - 3
f(2x + 4) = 4x² + 8x - 3

misal
2x + 4 = p
2x = p - 4
x = (p - 4) / 2
x = p/2 - 2

maka
f(p) = 4(p/2 - 2)² + 8(p/2 - 2) - 3
f(p) = 4(p/2 - 2)(p/2 - 2) + 4p - 16 - 3
f(p) = 4(p²/4 -2p + 4) + 4p - 19
f(p) = p²- 8p + 16 + 4p - 19
f(p) = p² - 4p - 3
f(x) = x² - 4x - 3


Nilai f(-2)
f(-2) = (-2)² -4(-2) - 3 = 4 + 8 - 3 = 9