1 / 22

One-to-One Functions; Inverse Function

One-to-One Functions; Inverse Function. A function f is one-to-one if for each x in the domain of f there is exactly one y in the range and no y in the range is the image of more than one x in the domain.

ailsa
Télécharger la présentation

One-to-One Functions; Inverse Function

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. One-to-One Functions; Inverse Function

  2. A function f is one-to-one if for each x in the domain of f there is exactly one y in the range and no y in the range is the image of more than one x in the domain. A function is not one-to-one if two different elements in the domain correspond to the same element in the range.

  3. x1 y1 x1 y1 x2 y2 x2 x3 x3 y3 y3 Domain Range Domain Range One-to-one function NOT One-to-one function x1 y1 y2 x3 y3 Not a function Domain Range

  4. M:Mother Function is NOT one-one Joe Samantha Anna Ian Chelsea George Laura Julie Hilary Barbara Sue Humans Mothers

  5. S: Social Security function IS one-one Joe Samantha Anna Ian Chelsea George 123456789 223456789 333456789 433456789 533456789 633456789 Americans SSN

  6. Is the function f below one – one? 10 11 12 13 14 15 16 1 2 3 4 5 6 7

  7. Use the graph to determine whether the function is one-to-one. Not one-to-one.

  8. Theorem Horizontal Line Test If horizontal lines intersect the graph of a function f in at most one point, then f is one-to-one.

  9. Use the graph to determine whether the function is one-to-one. One-to-one.

  10. The inverse of a one-one function is obtained by switching the role of x and y

  11. The inverse of the social security function Joe Samantha Anna Ian Chelsea George 123456789 223456789 333456789 433456789 533456789 633456789 SSN Americans

  12. Let and Find

  13. g is the inverse of f.

  14. Let f denote a one-to-one function y = f(x). The inverse of f, denoted by f -1 , is a function such that for every x in the domain of f and for every x in the domain of f-1. .

  15. Domain of f Range of f

  16. Theorem The graph of a function f and the graph of its inverse are symmetric with respect to the line y = x.

  17. y = x (0, 2) (2, 0)

  18. Finding the inverse of a 1-1 function Step1: Write the equation in the form Step2: Interchange x and y. Step 3: Solve for y. Step 4: Write for y.

  19. Find the inverse of Also find its domain and range Step1: Step2: Interchange x and y Step 3: Solve for y

More Related