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Inverse Functions

This lesson focuses on understanding inverse functions, their composition, and how to effectively solve related equations. Students will engage in a warm-up exercise by solving equations like 2(x - 1) = 6 and learn to compute the inverse of given functions step by step. The objectives include verifying if two functions are inverses and justifying results. Through examples and practice, learners will grasp the crucial concepts behind functions and their inverses, preparing them for more complex problems.

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Inverse Functions

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  1. Inverse Functions Algebra 2

  2. Warm Up Your Engine! • Solve the following equations. Show all work! 1. 2(x – 1) = 6 2. 3.

  3. Standard Course of Study Objective 2.01 Use the composition and inverse of functions to model and solve problems; justify results.

  4. Lesson Objectives What I will learn: • Compute the inverse function for a given function • Verify if two functions are inverses

  5. What do we remember about…. FUNCTIONS?

  6. What do we remember about… INVERSE?

  7. Let’s put those concepts together. Inverse Functions: Two functions that completely undo each other leaving only x.

  8. Examples: Find the inverse for the given function. 1.

  9. 1. Step 1: Switch x and y Step 2: Solve the equation for y

  10. 2.

  11. How can we check?

  12. Too easy? Find the inverse function for: 3.

  13. 4.

  14. Even harder! 5.

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