I'm looking for a way to find the inverse of a function that resembles something like this, ${f(x)=x^{3}+4x+2}$. So one of the “form” $f(x)=x^{3}+ax+b$.
I am told that it has an inverse function, $ $ $ f^{-1}(x)$ , and that $f(0)=2$.
Can someone point me in the right direction?
The problem, as you told me in the comments, consists in computing $(f^{-1})'(2)$. Since $f(0)=2$, $f^{-1}(2)=0$, and therefore$$(f^{-1})'(2)=\frac1{f'\bigl(f^{-1}(2)\bigr)}=\frac1{f'(0)}=\frac14.$$You don't have to determine $f^{-1}(x)$ for every $x$ in order to do this.