The rational function .

Horizontal line test :

A function is one-to-one if and only if no horizontal line intersects its graph more than once.

Graph :

Draw the coordinate plane.

Graph the function .

Draw the horizontal line  .

Observe the graph: the horizontal line  touches the graph of the function exactly one point.

Therefore, the function is one-to-one.

The function is one-to-one on its entire domain and therefore has an inverse function.

The function is one-to-one.

Inverse function exists.