Question

Diketahui g(x) = x² - 2x
(f○g) (2x - 1) = 16x² - 32x + 14. Tentukan f(x)

Answer 1

(fog) (2x-1)= 16x²-32x+14

misal t = 2x-1
maka
2x= t+1
x= t+1 / 2

(fog) (x) = 16(t+1 / 2)² - 32(t+1 / 2) + 14
= 4(t²+2t+1) - 16(t+1)+14
= 4t²+8t+4-16t-16+14
= 4t²-8t+2
(fog) (x) = 4x²-8x +2
f(x²-2x)(x)= 4x²-8x+2
misalkan t=x²-2x
maka
t=x²-2x
t+1= x²-2x+1
t+1= (x-1)²
√(t+1) = x-1
x-1= √(t+1)
x= 1+ √(x+1)

f(x) = 4(1+√(x+1)² - 8(1+√(x+1)+2
= 4(1+2√(x+1) + x+1 ) - 8-8√(x+1) +2
= 8+2√(x+1) +x -6 - 8√(x+1)
= -6√(x+1) + x