1 / 31

Inverses of Functions

Inverses of Functions. Warm Up #1 – Find the following. Answer to a. Answer to b. Answer to c. Answer to d. Answer to e. Answer to f. Answer to g. Warm Up #2 - Determine whether the statement is true or false. Justify your answer. FALSE!.

sgorman
Télécharger la présentation

Inverses of Functions

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Inverses of Functions

  2. Warm Up #1 – Find the following.

  3. Answer to a

  4. Answer to b

  5. Answer to c

  6. Answer to d

  7. Answer to e

  8. Answer to f

  9. Answer to g

  10. Warm Up #2 - Determine whether the statement is true or false. Justify your answer. FALSE!

  11. Warm Up #3: Graph & give the domain & range. Answer on Next Slide

  12. Warm Up #3: Graph & give the domain & range. x y x -3 -4 -5 2 1 0 1 2 3 4 -3 -2 -1 0

  13. Inverse of a relation • The inverse of the ordered pairs (x, y) is the set of all ordered pairs (y, x). • The Domain of the function is the range of the inverse and the Range of the function is the Domain of the inverse. • Symbol: In other words, switch the x’s and y’s!

  14. Example: {(1,2), (2, 4), (3, 6), (4, 8)} Inverse:

  15. Function notation? What is really happening when you find the inverse? Find the inverse of f(x)=4x-2 *4 -2 x 4x-2 (x+2)/4 /4 +2 x So

  16. To find an inverse… • Switch the x’s and y’s. • Solve for y. • Change to functional notation.

  17. Find Inverse:

  18. Find Inverse:

  19. Find Inverse:

  20. Find Inverse:

  21. Draw the inverse. Compare to the line y = x. What do you notice?

  22. Graph the inverse of the following: The function and its inverse are symmetric with respect to the y-axis. x y 0 -3 1 1 -5 -4 2 4

  23. Things to note.. • The domain of is the range of f(x). • The graph of an inverse function can be found by reflecting a function in the line y=x. Check this by plotting y = 3x + 1 and on your graphic calculator. Take a look

  24. Reflecting..

  25. Find the inverse of the function. Is the inverse also a function? Let’s look at the graphs. NOTE: Inverse is NOT a function! Inverse

  26. Horizontal Line Test • If a horizontal line only passes through one point at a time, then the inverse of the function will also be a function.

  27. Composition and Inverses • If f and g are functions and then f and g are inverses of one another. !!!!!!!!!!!!!!!!!!!!!!

  28. Example: Show that the following are inverses of each other. The composition of each both produce a value of x; Therefore, they are inverses of each other.

  29. Are f & g inverses?

  30. You Try…. • Show that • are inverses of each other.

  31. Are f & g inverses?

More Related