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 a graph is a function then it passes the vertical line test ie the graph cuts a given vertical line atmost $1$ time. But as here our graph is of $\arcsin (x) $ which ust oscillates between $\frac {-\pi}{2},\frac {\pi}{2} $. Hence the given condition isnt a function on any domain.
