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08 inverse functions - y = f x is a function(i.e y = f x...

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Inverse Relations If y = f ( x ) is a relation , then the inverse relation obtained by interchanging x and y is x = f ( y ) 3 e.g. y x x = + The domain of the relation is the range of its inverse relation A relation and its inverse relation are reflections of each other in the line y = x . 2 e.g. y x = 3 inverse relation is x y y = + The range of the relation is the domain of its inverse relation domain: all real x range: 0 y 2 inverse relation: x y = domain: 0 x range: all real y
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Inverse Functions If an inverse relation of a function, is a function, then it is called an inverse function . Testing For Inverse Functions (1) Use a horizontal line test OR ( 29 ( 29 ( 29 ( 29 unique. is , as rewritten is When 2 x g y x g y y f x = = = ( 29 2 x y i = y x Only has an inverse relation OR 2 y x = x y ± = NOT UNIQUE y x ( 29 3 x y ii = Has an inverse function OR 3 y x = 3 x y = UNIQUE
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Unformatted text preview: y = f ( x ) is a function, (i.e. y = f ( x ) has an inverse function), then; ( 29 ( 29 x x f f =-1 AND ( 29 ( 29 x x f f =-1 e.g. ( 29 2 2 x f x x-= + 2 2 2 2 x y y x x y--= ⇒ = + + ( 29 ( 29 2 2 2 2 1 2 2 2 2 1 y x y xy x y x y x x y x + =-+ =--= --+ =-( 29 ( 29 1 2 2 2 2 2 1 2 x x f f x x x-- + ÷ + =- - ÷ + 2 4 2 4 2 2 4 4 x x x x x x- + + = + - + = = ( 29 ( 29 1 2 2 2 1 2 2 2 1 x x f f x x x-+ - ÷- = + + ÷- 2 2 2 2 2 2 2 2 4 4 x x x x x x + - + = + + -= = ( ii ) Draw the inverse relation y x Exercise 2H; 1aceg, 2, 3bdf, 5ac, 6bd, 7ac, 9bde, 10adfhj...
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