Section 9.1 Composite and Inverse Functions  Composite Functions (f◦g)(x)=f(g(x))  Inverses and 1-to-1 Functions  Finding Formulas for Inverses  Graphing.

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Presentation transcript:

Section 9.1 Composite and Inverse Functions  Composite Functions (f◦g)(x)=f(g(x))  Inverses and 1-to-1 Functions  Finding Formulas for Inverses  Graphing Functions and Their Inverses  Inverse Functions and Composition 9.11

Two Functions: Concept and Notation for Composition 9.12

Women’s Shoe Sizes 9.13

Is Composition Commutative? 9.14

Inverses and One-to-One Functions 9.15

Does an Inverse Function Exist? Tests for One-To-One Functions 9.16

Thinking about Inverse Functions  Do all Linear Functions have Inverse Functions?  All except Horizontal and Vertical Lines  What about Quadratic Functions (Parabolas)?   No: y=4 fails HLT 9.17

Inverse Function Notation: f -1 (x) 9.18

Graphing Functions & Their Inverses 9.19

Consider g(x) = x and g -1 (x)  Is g(x) one-to-one? 9.110

Inverse Functions and Composition 9.111

What Next? Exponential Functions  Present Section 9.2 Present Section