Question

G(x) = 2x+3
(fog)(x) = 12x^2 + 32x + 26 tentukan f(2)
dengan caranya

Answer 1

Verified answer

Cara 1
g(x)     = 2
2x + 3 = 2
      2x = -1
        x = - 1/2

(fog)(x) = 12x² + 32x + 26
  f(g(x)) = 12(-1/2)² + 32(-1/2) + 26
             = 3 - 16 + 26
             = 13
     
cara 2
invers dari g(x) = 2x + 3 adalah 1/2(x - 3)
maka f(x) = 12 (1/2(x - 3))² + 32(1/2(x - 3)) + 26
                = 12 (1/4 ( x² - 6x + 9) + 16x - 48 + 26
                = 3x² - 18x + 27 + 16x - 48 +26
                = 3x² - 2x + 5
               
f(2) = 3( 2)² - 2(2) + 5
       = 12 - 4 + 5
       = 13