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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 1. Solution y 3 x 1 Write original equation. x 3 y 1 Switch x and y . x 1 3 y Add 1 to each side. 1 3 x 1 3 y Divide each side by 3 . The inverse relation is y 1 3 x 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 1 , read as “ f inverse.” 162 Algebra 2 Notetaking Guide Chapter 7
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Your Notes Verify that f ( x ) 3 x 1 and f 1 ( x ) 1 3 x 1 3 are inverses. Solution Show that f ( f 1 ( x )) x and f 1 ( f ( x )) x . f ( f 1 ( x )) f 1 3 x 1 3 f 1 ( f ( x )) f 1 (3 x 1) 3 1 3 x 1 3 1 1 3 (3 x 1) 1 3 x 1 1 x 1 3 1 3 x x Example 2
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