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Algebra 2 7.4 Notes

# Algebra 2 7.4 Notes - 7.4 Inverse Functions Goals p Find...

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Inverse Functions Goals p Find inverses of linear functions. p Find inverses of nonlinear functions. 7.4 VOCABULARY Inverse relation A relation that maps the output values of an original relation back to their original input values Inverse functions A relation and its inverse relation whenever both relations are functions Your Notes Example 1 Finding an Inverse Relation Find an equation for the inverse of the relation y ± 3 x ² 1. Solution y ± 3 x ² 1 Write original equation. x ± 3 y ² 1 Switch x and y . x ³ 1 ± 3 y Add 1 to each side. ´ 1 3 ´ x ³ ´ 1 3 ´ ± y Divide each side by 3 . The inverse relation is y ± ´ 1 3 ´ x ³ ´ 1 3 ´ . INVERSE FUNCTIONS Functions f and g are inverse functions of each other provided: f ( g ( x )) ± x and g ( f ( x )) ± x The function g is denoted by f ² 1 , read as “ f inverse.” 162 Algebra 2 Notetaking Guide • Chapter 7

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Your Notes Verify that f ( x ) ± 3 x ² 1 and f ² 1 ( x ) ± ³ 1 3 ³ x ´ ³ 1 3 ³ are inverses.
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Algebra 2 7.4 Notes - 7.4 Inverse Functions Goals p Find...

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