Question

Diketahui g(x) = 2x-1 dan (f o g ) (x)= 4xkaudrat -6x 10 . nilai f(3)

Answer 1

G(x) = 2x - 1
(fog)(x) = 4x² - 6x + 10
f(3) = ............?

Penyelesaian :

g⁻¹(x) = (x + 1)/2

(fog)(x) = f(g(x)
4x² - 6x + 10 = f(2x - 1)
f(x) = (fog)(g⁻¹(x))
     = 4[(x + 1)/2]² - 6[(x + 1)/2] + 10
     = 4[(x² + 2x + 1)/4] - 3(x + 1) + 10
     = x² + 2x + 1 - 3x - 3 + 10
     = x² - x + 8

f(x) = x² - x + 8
f(3) = 3³ - 3 + 8
       = 9 - 3 + 8
       = 14

Jadi, niali dari f(3) adalah 14