The graph of the function is shown.
Use the graph to show that f(x) is invertible. Then, determine the inverse, and graph both functions.
Graphically, it can be shown that a function is invertible by performing the horizontal line test. If we move an imaginary horizontal line across the graph of a function, and the line intersects the graph more than once anywhere, the function is not invertible. Here, we'll draw more than one line to be sure.
The domain of f(x) is restricted to x≥0. As a consequence, the domain of must be restricted to the same interval, even though is defined for all values of x.