Mathematics - Functions Question with Solution | TestHub

We have, $\frac{1}{2}gof(x)=2x^2-5x+2$ $\begin{array}{rl}& \Rightarrow g(f(x))=4x^2-10x+4\\ & \Rightarrow (f(x){)}^2+f(x)-2=4x^2-10x+4\\ & \Rightarrow (f(x){)}^2+f(x)-\left(4x^2-10x+6\right)=0\\ & \Rightarrow f(x)=\frac{-1\pm \sqrt{1+4\left(4x^2-10x+6\right)}}{2}\\ & \Rightarrow f(x)=\frac{-1\pm \sqrt{16x^2-40x+25}}{2}\\ & \Rightarrow f(x)=\frac{-1\pm (4x-5)}{2}=2x-3,-2x+2\end{array}$ Hence, $f(x)=2x-3$