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Section 3.6 class notes_0

Section 3.6 class notes_0 - Section 3.6 One-to-one...

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× × × × × × × × × × ( ) y f x = ( ) y g x = Section 3.6 One-to-one Functions; Inverse Functions Objective 1 : Understanding the Definition of a One-to-one Function Definition One-to-one Function A function f is one-to-one if for any values a b in the domain of f , ( ) ( ) f a f b . Interpretation: For a function f(x) = y , we know that for each x in the Domain there exists one and only one y in the Range. For a one-to-one function f(x) = y, for each x in the Domain there exists one and only one y in the Range AND for each y in the Range there exists one and only one x in the Domain. Objective 2 : Determining if a Function is One-to-one Using the Horizontal Line Test The Horizontal Line Test If every horizontal line intersects the graph of a function f at most once, then f is one-to-one. 3.6.4 and 16 Determine whether the given functions are one-to-one. a) b)

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f 1 f - Objective 3: Understanding and Verifying Inverse Functions Every one-to-one function has an inverse function.
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Section 3.6 class notes_0 - Section 3.6 One-to-one...

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