To have an inverse function, a function f must be

It simply must pass through a horizontal line. aka the x-axis 

To inverse a function, the given function must pass a few requirements;

The graph of the function must pass the horizontal and vertical test. This means, if a horizontal line is drawn anywhere on the graph, it should only intersect with one point. Similarly with the vertical line test, if a line is drawn vertically on the graph, it should intersect with one point only. If the given function passes these rules, it's inverse can be found. Just for your information, vertical and horizontal line tests are real and used to find such information. 

Hope I helped :)