Question

find f(x)
g (x) = x² + x - 2 and (gof) (x) = 4x² -10x + 4​

Answer 1

Answer:

2x-3

Step-by-step explanation:

given g(x)=x²+x-2

and gof(x)=4x²-10x+4=>g(f(x))=4x²-10x+4...(1)

g(f(x)) is also equal to f(x)²+f(x)-2...(2)

from 1 and 2 we get

f(x)²+f(x)-2=4x²-10x+4

f(x)²-f(x)+2f(x)-2=4x²-8x-2x+4

f(x)²+f(x)+(1/2)²=4x²-10x+4+2+(1/2)²

(f(x)+1/2)²=4x²-10x+6+1/4

(f(x)+1/2)²=4x²-10x+25/4=(2x-5/2)²

f(x)+1/2=2x-5/2

f(x)=2x-3