Consider the functions. Find if
Determine if the two functions are inverses of each other.
The two functions, and are inverses if Thus, if we can show that
The graph of the function is shown.
Use the graph to show that 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 is restricted to As a consequence, the domain of must be restricted to the same interval, even though is defined for all values of