3.6 Inverse Functions

3.6 Inverse Functions - Inverse Functions Inverse Section...

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Unformatted text preview: Inverse Functions Inverse Section 3.6 Graphs of Inverse Relations Graphs Let f be a function. If (a, b) is a point o the Let (a, graph of f, then (b, a) is a point o the graph of its inverse. of The graph of the inverse of f is a reflection of The the graph of f across the line y = x. One-to-One Functions One-to-One A function f is one-to-one if f(a) = f(b) iimplies that a = b. mplies b. If a function is one-to-one, then its If inverse is also a function. inverse Use the horizontal line test to determine if Use a function is one-to-one function Not one-to-one One-to-one Composition of Inverse Functions Functions A one-to-one function f and its inverse function f −1 one-to-one have these properties. have f −1 o f ) ( x) = x ( ( f o f ) ( x) = x −1 for every x in the domain of f. for f −1 for every x in the domain of Also, any two functions having both properties are one-to-one and are inverses of each other. one-to-one Joke Time Joke What’s a cow’s favorite What’s painting? painting? The Moona Lisa What does the tooth fairy give for half a tooth? for Nothing. She wants the tooth, Nothing. the whole tooth, and nothing but the tooth! but ...
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This note was uploaded on 12/01/2011 for the course MATH 111 taught by Professor Stuff during the Winter '11 term at BYU.

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