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7.7 - – We can switch the variables then solve y = x 2 3...

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1 7.7 Inverse Relations and Functions Find the following function values: Find f(g(x)) Find g(f(x)) Find f(g(0)): Find g(f(0)): 1 ) ( + = x x f x x g 1 ) ( = Warm Up What’s the domain? Objective To find the inverse of a function. To use the composition of inverse functions. Relationship Investigation Find g(f(-3)): Find f(g(6)): Find g(f(10)): Find f(g(10)): f ( x ) = 2 x - 8 g ( x ) = x + 8 2 What Are Inverse Relations? They “undo” each other. When we combine inverse relations or operations, the end result is the initial input. What is the inverse of: + 8 The inverse of: multiplying by 3? Inverse Functions • Find: f ( x ) = 2 x - 8 g ( x ) = x + 8 2 ( f o g )( x ) = ( g o f )( x ) =
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2 Composition of Inverse Functions Property What is the composition of inverse functions? ( f - 1 o f )( x ) = ? ( f - 1 ( f ( x )) = ? Inverse Relations X Y -1 0 0 2 2 4 3 8 Relation s Y X 0 ___ 2 ___ 4 ___ 8 ___ Inverse of s Domain and Range? Finding The Inverse • SHORTCUT:
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Unformatted text preview: – We can switch the variables then solve! y = x 2 + 3 y-1 = ? Is the inverse a function? You Try HW#7 • Find the Inverse of: y = 4 - 3x Is the inverse a function? Graphing Functions y = x 2 + 1 y = ± x-1 Domain and Range? Graphing You Try HW#18 • Graph the relation and its inverse. y = -x 2 y-1 = ? Domain and Range? 3 Practice Work • P. 404 7-11, 15, 17-20, 23-29, – If you get hung up, try a similar odd numbered problem; then check your answer in the back of the book to measure your understanding. Inverse - You Try #25 • Find f inverse, the domain and range of both, and determine if it is a function. f ( x ) = x + 7 Graphing - You Try #19 • Graph each relation and its inverse y = 4 x 2-2...
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