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Exploring Inverses of Functions: Algebraic Methods

Learn about finding inverse functions algebraically by switching input and output values. Practice verifying functions as inverses. Complete independent exercises for thorough understanding.

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Exploring Inverses of Functions: Algebraic Methods

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  1. Inverses of FunctionsPart 3 Lesson 2.10

  2. Oral Drill • What are two other ways to refer to the input? • What are two other ways to refer to the output? • j

  3. Oral Drill • k • l • m • n • p

  4. What is the inverse of a function? • The relation that results when the input and the output are switched. • x switches with y • Domain switches with range

  5. Finding Inverses AlgebraicallyExample #1 Find Change to x-y notation. Less confusing Switch input and output. To find inverse Subtract 2 from both sides. To solve for y Divide both sides by 2. To solve for y. Distribute and rearrange. To simplify right side of equation.

  6. Practice #1.a • . Find

  7. Practice #1.b • . Find

  8. Independent Practice • Complete Problem 1, 2, 3 independently. • If you have time: 6, 8

  9. Verifying (proving) functions are inversesExample #2 You are given the problem and find that . Verify (prove) these functions are inverses. Process: • Call by the name . • Find and . • If and , the functions are inverses of each other.

  10. Practice #2.a • With your table, verify the following functions are inverses: HINT: Write as for one equation and for the other.. . . . . . . . . .

  11. Independent Practice • Complete problems 4, 5, 7 independently. • Complete 6, 8 if you did not before

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