(gοf)(x)=4x2−10x+4 And, (f(x)2)+f(x)−2=4x2−10x+4 For the function to be linear f(x)=ax+b so, (ax+b)2+(ax+b)−2=4x2−10x+4 a2x2+(2ab+a)x+(b2+b−2)=4x2−10x+4 By the comparison of coefficients, a2=4 And, 2ab+a=−10 And, b2+b−2=4 So, a±2 Then, b={
−3;
ifa=2
2;
ifa=−2
These values satisfies above relations, thus, f(x)=2x−3or−2x+2