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6-2: Inverse Functions & Relations

6-2: Inverse Functions & Relations. Learning Target. I can… Find the inverse of a given relation or function. Relations. Relation: Set of Ordered Pairs Ex: {(1, 3) (2, -5) (0, 0) (3, -6) (2, 8)} Inverse Relation: Obtained by switching the x and y coordinates

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6-2: Inverse Functions & Relations

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  1. 6-2: Inverse Functions & Relations

  2. Learning Target • I can… • Find the inverse of a given relation or function.

  3. Relations • Relation: Set of Ordered Pairs Ex: {(1, 3) (2, -5) (0, 0) (3, -6) (2, 8)} • Inverse Relation: Obtained by switching the x and y coordinates Ex: {(3, 1) (-5, 2) (0, 0) (-6, 3) (8, 2)}

  4. Examples • Find the inverse of each relation: 1. {(10, 3) (7, -4) (8, 20)} 2. {(4, 1) (-3, 3) (7, 0) (-1, 1)} 3. {(2, 2) (9, -7) (-2, -3) (1, -3)}

  5. Answers 1. {(3, 10) (-4, 7) (20, 8)} 2. {(1, 4) (3, -3) (0, 7) (1, -1)} 3. {(2, 2) (-7, 9) (-3, -2) (-3, 1)}

  6. Functions • Inverse Functions: Obtained by exchanging the x and y variable in the equation. Steps: 1. Replace f(x) with y. 2. Switch x and y. 3. Re-solve the equation for y. 4. Replace y with f-1(x).

  7. Examples • Find the inverse of

  8. Find the inverse of

  9. Examples • Find the inverses for the following functions:

  10. Answers

  11. Answers

  12. Homework • Pg 396 #9-22 all

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