So I know how to find the inverse by switching $x$ with $y$ and solving for $y$ but I'm not sure what to do when the function has a sum of variables, for example:
$$f(x)= 2\ln(x+1)+xe^x−2x^2+1$$ $$f(x)=3\sin(\frac{\pi}{2}x)−x^3e^{(x−1)}−2x$$
Do I find separate inverses and then add them again or am I just worse than I thought at this? I can't solve for $y$ and get a simple $y=\cdots$ or can I?
Also I found there's a way to not do this when the question asks for a specific point like $f^{-1}(2)$ but most of my questions ask for the derivative of the inverse like $(f^{-1})'(2)$ is there a simpler way to solve this too?
I don't have enough reputation to comment on your post and so, to help you with your question I have to write down a solution. But what I am writing is more of a hint.
You can apply inverse function theorem. That is, whenever your function satisfies the assumptions of this theorem, you can find $(f^{-1})'(y)$ using the following formula: $$ \left(f^{-1}\right)^{\prime}(y)=\frac{1}{f^{\prime}(x)}=\frac{1}{f^{\prime}\left(f^{-1}(y)\right)} $$ Hope this helps and answers your question.