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Inverse Relations and Functions

Inverse Relations and Functions. 7.8. Vocabulary. relation inverse relation The inverse function of f is denoted as f -1. Find the inverse of this relation. State the domain and range. Ex 1. {(1 , 3) , (6 , 3) , (6 , 0) , (1 , 0)}. Ex 2. x -1 0 1 2

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Inverse Relations and Functions

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  1. Inverse Relationsand Functions 7.8

  2. Vocabulary relation inverse relation The inverse function of fis denoted as f-1.

  3. Find the inverse of this relation. State the domain and range. Ex 1 {(1, 3), (6, 3), (6, 0), (1, 0)} Ex 2 x -1 0 1 2 y -2 -1 -1 -2

  4. Finding the Inverse of a Function • Replace f (x) with y • Interchange x and y • Solve for y • Replace y with f -1 (x)

  5. Ex 3 Find the inverse of . Find the domain and range then graph both.

  6. Ex 4 Find the inverse of . Find the domain and range.

  7. Ex 5 Find the inverse. Find the domain and range then graph both.

  8. Ex 6 Find the inverse. Find the domain and range then graph both. y = (x+3)2 – 2; x ≤ -3

  9. Ex 7 Find the inverse. Find the domain and range then graph both.

  10. Verifying Inverse Functions Two functions are inverse functions if and only if their compositions are the identity function { I (x) = x }. OR

  11. Ex 8 Determine if the functions are inverse functions.

  12. Ex 9 Determine if the functions are inverse functions.

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