The following condition fails to define a function on any domain. State. why?" $\sin f(x) =x$ 
Quoting" The following condition fails to define a function on any domain. State. why?"
$$\sin f(x) =x$$

I understand that it yields a sinusoid oscillating vertically defined between $x=-1$ and $x=1$.
It shows that $\forall x \in [-1,1]$, many values of y is mapped onto.
Because there is no unique image for a specific value of $x$, it fails to define a function.
Is there a more formal approach more appropriate for a real analysis class? or is there an alternative explanation?
Any input is much appreciated.

If $|x|\leq 1$ the statement $\sin f(x)=x$ does not DEFINE $f(x)$ although the statement may be a property of a function $f.$  There are infinitely many $y$ for which $\sin y=x$ and the statement $\sin f(x)=x$ does not tell you which one of these $y$ is actually $f(x).$
