Let $\displaystyle \mathbb{R} \rightarrow [-1,1]$ be defined by $\displaystyle f(x) = sin x$. How many distinct right inverses can you find?
I am lost as to where to start
This question has already been asked, and I think a good hint has been given. Why don't you post your thoughts about it?
$\displaystyle g(x) = \sin^{-1}(x)$ is one solution. What about $\displaystyle g(x) = \sin^{-1}(x) + 2\pi$?