Let $f:R\to R,g:R\to R$ be two functions given by$f\left(x\right)=2x-3,g\left(x\right)=x^3+5$ . Then ${\left(fog\right)}^{-1}\left(x\right)$ is equal to:

Let $y=\left(fog\right)\left(x\right)=f\left[g\right(x\left)\right]=f(x^3+5)$

                                           $=2(x^3+5)-3=2x^3+7$

$\therefore x^3=\frac{y-7}{2}$

$\Rightarrow x={\left(\frac{y-7}{2}\right)}^{1/3}$ $\Rightarrow {\left(fog\right)}^{-1}\left(y\right)$ $={\left(\frac{y-7}{2}\right)}^{1/3}$

$\Rightarrow {\left(fog\right)}^{-1}\left(x\right)$ $={\left(\frac{x-7}{2}\right)}^{1/3}$