If g(x)=x^2+x-2 and 1 2 (g f)(x)=2 x^2-5 x+2 , then one such function f(x)=

Step-by-step solution

Given, g(x)=x^2+x-2 and aligned & 1 2 (g f)(x)=2 x^2-5 x+2 & g(f(x))=4 x^2-10 x+4 & (f(x))^2+(f(x))-2=4 x^2-10 x+4 & aligned Now, it is necessary that f(x) should be linear polynomial expression, so let f(x)=a x+b , then array r (a x+b)^2+(a x+b)-2=4 x^2-10 x+4 a^2 x^2+(2 a b+a) x+ (b^2+b-2 ) =4 x^2-10 x+4 array On comparing the coefficient of different kind of terms, we are getting aligned & a^2=4 , & 2 a b+a=-10 & and b^2+b-2=4 & aligned So, then aligned & a= 2, & b= aligned -3 ; & if a=2 2 ; & if a-2^ aligned .