In general,
A function graph must not pass above or below itself.
Therefore, for its inverse to be a function, it must not
pass either to the right or left of itself.
Or ---
A function graph must pass the vertical line test. That is,
no vertical line can intersect the graph more than once.
Therefore, in order for a function to have an inverse which
is also a function, its graph must pass the horizontal line
test. That is, no horizontal line can intersect the graph
more than once.
Edwin