For a function $f\left(x\right)=tanx+3x^2$ at $a=0$, find $ \left(f^{-1}\right)'\:\left(a\right)$
Given context of a chapter Derivatives of Inverse Functions I am trying to approach question with $\left(f^{-1}\right)'\left(a\right)=\frac{1}{f'\left(f^{-1}\left(a\right)\right)}$
The solution requires $f^{-1}\left(a\right)$
Currently I don't have approach to find inverse $tanx+3x^2$ in general. Another idea that i had was to conditionally equate
$a=0=\:tanx+3x^2$
and solve for x, sadly I don't have approach to solve that as well.
I have feeling that i completely missed the point of the chapter, because i have similar struggles with most of the chapter's exercises, though I was lucky to be able to evaluate at least one of above so far.
I would be very thankful if your answer will help me see what I miss for the topic in general.
Source: Exercise 272 in openstax Calculus vol.1