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Section 2.6 – Inverse Functions

Section 2.6 – Inverse Functions. DOES an inverse function exist?. IF YES , you can find the inverse function. The inverse function is denoted by. The Existence of the Inverse of f(x). IF for every x there is at most one y (function). AND.

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Section 2.6 – Inverse Functions

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  1. Section 2.6 – Inverse Functions

  2. DOES an inverse function exist? IF YES, you can find the inverse function.

  3. The inverse function is denoted by The Existence of the Inverse of f(x) IFfor every x there is at most one y(function) AND IFfor every y there is at most one x(one-to-one) then an inverse function of f(x) exists.

  4. Graphical Existence of Inverse Passes BOTH vertical and horizontal line test. No Inverse Exists (1, 0), (0, 0) No Inverse Exists (1, 1), (-1, 1) Inverse Exists

  5. Inverse Exists No Inverse Exists (3, 0.9), (7, 0.9)

  6. Inverse Exists Inverse Exists

  7. No Inverse Exists (-3, 2), (0, 2) No Inverse Exists (2, -2), (2, 5)

  8. Ford Bush Carter Clinton President Vice-President January February March July Winter Spring Summer Does an inverse exist? No Inverse Exists (1, 2), (2, 2) No Inverse Exists (Jan, Winter), (Feb, Winter) No Inverse Exists (2, 4), (3, 4) No Inverse Exists (Ford, President), (Ford, Vice-President) No Inverse Exists (6, 5), (6, 3)

  9. Algebraic Existence of Inverse Inverse Exists No Inverse Exists (-4, -12), (-2, -12) No Inverse Exists (4, 2), (4, -2) No Inverse Exists (0, 2), (0, -2) No Inverse Exists (4, 0), (-4, 0)

  10. 3. Replace y with FINDING the inverse which exists 1. Switch the x and the y. 2. (Algebraically) Solve for y.

  11. Finding the inverse function GRAPHICALLY

  12. No Inverse Exists (5, 4), (7, 4) Finding the Inverse Function TABULARLY

  13. Finding the Inverse ANALYTICALLY

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