PP 7.1 - Inverse Functions One-to-One Function A function...

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Inverse Functions
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One-to-One Function 1 3 ) ( + = x x f A function is one-to-one if it never takes on the same value twice. That means that if f(a) = f(b) and f is one-to-one, then a = b . Example: is one-to-one because b a b a b a = = + = + 3 3 1 3 1 3
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g(-2). 4 g(2) since one - to - one NOT is ) ( : Example 2 = = = x x g One-to-one NOT one-to-one
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Horizontal Line Test A function is one-to-one if and only if no horizontal line intersects its graph more than once.
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Inverse Function Let f be a one-to one function with domain A and range B. Then its inverse function has domain B and range A and it is defined by y x f x y f = = - ) ( ) ( 1 1 1 domain range range domain - - = = f f f f [ ] 1 1 ) ( ) ( 1 ) ( - - = x f x f x f
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Example functions. inverse are ) ( and , 0 , ) ( 2 x x g x x x f = = g f g f domain ) [0, range range ) , 0 [ domain = = = = 0 , ) ( 0 , | | ) ( 2 2 2 = = = = a a a f a a a a a g
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Cancellation Equations x x f f x f f = = - - )) ( ( )) ( ( 1 1 functions. inverse
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This note was uploaded on 01/21/2011 for the course PHYS 4A 60865 taught by Professor L. oldewurtel during the Fall '09 term at Irvine Valley College.

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PP 7.1 - Inverse Functions One-to-One Function A function...

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