# Left Inverse vs Right Inverse

Consider a function $f(x)$ and its inverse $g(x)$.

Then $(f \circ g)(x) = x$ and $(g \circ f)(x) = x$

Are both these statements separate requirements in order for the inverse to be defined? Is it possible that one of the above statements is true but not the other? If so, could I see an example of such a case?

Otherwise, could you prove one having knowledge of the other?

Thanks!

BiP