I started with the definition of a right inverse.let $\displaystyle f: \Re \rightarrow [-1,1]$ be defined by $\displaystyle f(x)=sin x$. How many distinct right inverses acan you find?

$\displaystyle f(g(y))=y \ \forall \ y\in [-1,1]$

$\displaystyle sin(g(y))=y$

$\displaystyle g(y)=arcsin (y)$

Isn't this also it's inverse? Not only that, there is no room to find more so my answer is just one distinct right inverse.

Is something going wrong or should it turn out like this?