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 at .

Observe the graph :

The horizontal line  touches the graph of the function at more than one point, i.e,  and .

Therefore, the function is not one-to-one.

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

Since the function is not one-to-one on its entire domain and therefore inverse does not exist. 

Inverse function does not exists.