Q7SOL - MAP 103 Prociency Algebra Quiz#7 Fall 2009...

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MAP 103: Proficiency Algebra, Quiz #7, Fall 2009 SOLUTIONS 1. Let f ( x ) = 2 + 3 x x + 1 . Find a formula for the inverse f - 1 ( x ) and solve the equation f - 1 ( x ) = 2 .
2. Let g ( x ) = 1 1 ( x ) and show that g - 1 g ( x ) = x. What is the domain for g - 1 ( x )? 2 . Find a formula for the inverse g - 1 ( x ) and show that g - 1 g ( x ) = x. What is the domain for g - 1 ( x )?
We next verify that g - 1 g ( x ) = x. A computation follows. g - 1 g ( x ) = x (2 x + 1) (1 / 2 x - 1 / 2) = x 2 1 2 x - 1 2 + 1 = x x - 1 + 1 = x x = x It follows the domain of the inverse is D ( g - 1 ( x )) = ( -∞ , ) . 3. Let h ( x ) = e x + 2 . By reflecting the graph of h ( x ) over the line f ( x ) = x, sketch a graph for the inverse h - 1 ( x ) of h ( x

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