PP Section 3.6

# PP Section 3.6 - Inverse Functions A function f is said to...

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Inverse Functions

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A function f is said to be one-to-one if, for any choice of numbers x 1 and x 2 , x 1 x 2 , in the domain of f , then f ( x 1 ) f ( x 2 ). Which of the following are one - to - one functions? {(1, 1), (2, 4), (3, 9), (4, 16)} {(-2, 4), (-1, 1), (0, 0), (1, 1)} one-to-one not one-to-one
Theorem Horizontal Line Test If horizontal lines intersect the graph of a function f in at most one point, then f is one-to-one. Use the graph to determine whether the following function is one - to - one. 2 2 ) ( x x f = x y (0,0)

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Use the graph to determine whether the following function is one - to - one. x y (1,1) (-1,-1) x x f 1 ) ( =
f denote a one-to-one function y = f (x) . The inverse of f , denoted f -1 , is a function such that f -1 ( f ( x )) = x for every x in the domain f and f ( f -1 ( x )) = x for every x in the domain of f -1 . In other words, the function f maps each x in its domain to a unique y in its range. The inverse function

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## This note was uploaded on 01/22/2011 for the course MATH 2 taught by Professor Gardner during the Fall '08 term at Irvine Valley College.

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PP Section 3.6 - Inverse Functions A function f is said to...

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