9.2.2 Functions and Their Inverses (continued) Example 3 Determining Whether Functions are Inverses When both a relation and its inverse are functions, the relation is called a one-to-one function. In a one-to- one function, each y -value is paired with exactly one x -value. Composition of functions can be used to verify that two functions are inverses. Because inverse functions undo each other, the result of composing two inverses is the input value x . If the composition of two functions equals the input value, the functions are inverses.
If f ( g ( x )) = g ( f ( x )) = x , then f ( x ) and g ( x ) are inverse functions.
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