9.2.2 Functions and Their Inverses Key Objectives • Determine whether the inverse of a function is a function. • Write rules for the inverses of functions. Key Terms
• A one-to-one function is a function in which each y -value corresponds to only one x -value. The inverse of a one-to-one function is also a function.
Recall that the inverse of a function f ( x ) “undoes” f ( x ). The graph of the inverse of f ( x ) is a reflection of f ( x ) across the line y = x . The inverse of a function may or may not be a function. Example 1 Using the Horizontal-Line Test Recall that the vertical-line test can be used to determine whether a relation is a function by examining the number of times any vertical line passes through the graph of the relation. If any vertical line passes through the relation’s graph no more than one time, then the relation is a function. The horizontal-line test can be used to determine whether the inverse of a relation is a function. Horizontal-line Test If any horizontal line passes through more than one point on a graph of a relation, the inverse relation is not a function.
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