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Section 9.1 Composite and Inverse Functions

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. Two Functions: Concept and Notation for Composition.

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Section 9.1 Composite and Inverse Functions

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  1. 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 9.1

  2. Two Functions:Concept and Notation for Composition 9.1

  3. Women’s Shoe Sizes 9.1

  4. Is Composition Commutative? 9.1

  5. Inverses and One-to-One Functions 9.1

  6. Does an Inverse Function Exist?Tests for One-To-One Functions 9.1

  7. 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 9.1

  8. Inverse Function Notation: f -1(x) 9.1

  9. Graphing Functions & Their Inverses 9.1

  10. Consider g(x) = x3+ 2 and g -1(x) • Is g(x) one-to-one? 9.1

  11. Inverse Functions and Composition 9.1

  12. What Next? Exponential Functions • Present Section 9.2 9.1

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