Finding the inverse of trig functions

Question

I'm supposed to find the inverse of $$f(x) = \cos(x)+x$$

I usually just substitute $x$ for $y$ and then re-arrange. What do I do in this scenario?

Answer 1

You are trying to find $f^{-1}(1)$, which I will have set equal to $a$.

$$f^{-1}(1)=a$$

$$\implies1=f(a)$$

$$1=\cos(x)+x$$

By observation, $x=0$ is a solution.

By graphing, it is the only solution.