Question

if g(x









if g(x)=x^{2}+x-2 and (gof)=2x^{2}-5x+2 then f(x)=?

Answer 1

As f(x) is linear then assume, f(x) = ax + b.

then $gof = a^{2} x^{2} + a (1 + 2b)x + ( b^{2} + b - 2)$

Now compare and solve for a and b.
$a^{2} = 2$
$b^{2} + b - 2 = 2$

After getting a and b, just verify whether a(1 + 2b) = -5 or not.

As it's not verified so there are two possibilities.
(1) You have typed wrong function
(2) Answer is "No Such f(x) exists".