Horizontal line test :

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

The function is .

Draw a coordinate plane.

Graph the function .

Draw a horizontal line .

Observe the graph :

The horizontal line touches the graph of the function at .

Therefore, the function is one-to-one.

A function has an inverse function if and only if it is one-to-one.

Therefore, the inverse function exists.

The function is one-to-one and inverse exists.