Can someone give an example of another function whose inverse is only defined if you restrict the domain of the original function?

Answer 1

One example would be a quadratic function. This would not pass the horizontal line test because a horizontal line could hit the graph twice. Thus, you would have to restrict the domain of a quadratic function to half of it (either the left or right piece) in order to have an inverse defined.

For example if we use the function f(x)=x^2, we would have to restrict it to say x>=0.