1 / 20

4.1 Inverses Fri Oct 18

4.1 Inverses Fri Oct 18. Do Now Solve for Y 1) 2). Quiz Review. Retakes?. Inverses. When we go from an output of a function back to its inputs, we get an inverse relation Interchanging the first and second coordinates of each ordered pair produces the inverse relation. Notation.

cathy
Download Presentation

4.1 Inverses Fri Oct 18

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. 4.1 InversesFri Oct 18 Do Now Solve for Y 1) 2)

  2. Quiz Review • Retakes?

  3. Inverses • When we go from an output of a function back to its inputs, we get an inverse relation • Interchanging the first and second coordinates of each ordered pair produces the inverse relation

  4. Notation • The notation for the inverse of f(x) is • This is not an exponent!

  5. One-to-one Functions • A function f is one-to-one if different inputs have different outputs • If • Every y-value is unique

  6. Properties of one-to-one functions • If a function f is one-to-one, its inverse is a function • The domain of a one-tone function f is the range of its inverse • The range of a one-to-one function is the domain of its inverse • A function that is always increasing or decreasing is one-to-one

  7. Ways to show a function is one-to-one • 1) Assume f(a) = f(b); then show that a = b • If you can think of a y-value that has 2 x-values (ex: x^2 • 2) Horizontal Line Test • If a horizontal line intersects the graph more than once, it is NOT one-to-one

  8. How to find a formula for inverse • 1) Replace f(x) with y (if possible) • 2) Switch x and y • 3) Solve for y • 4) Replace y with

  9. Ex • Find an equation for the inverse of the relation

  10. Ex2 • Find an inverse for the function

  11. You try • Find an inverse for the following • 1) f(x) = 7 - x • 2) • 3)

  12. Closure • Find the inverse for the function • HW: p.356 #17-59 odds

  13. 4.1 Inverses and CompositionsMon Oct 21 • Do Now • Find the inverse of

  14. HW Review: p.356 #17-59 odds

  15. Inverses and Graphs • The graph of an inverse function is a reflection of f(x)’s graph across the line y = x

  16. Inverse Functions and Compositions • If a function f(x) is one-to-one, then the following compositions are true: for each x in the domain of f for each x in the domain of f inverse

  17. Ex • Given f(x) = 5x + 8, find its inverse and show they are inverses using composition

  18. Ex • Given , find its inverse and show they are inverses using composition

  19. Restricting the domain • In the case in which the inverse of a function is not a function, the domain can be restricted to allow the inverse to be a function • This is why square root graphs only show half of the true graph in a calculator

  20. Closure • Find the inverse of and show they are inverses using compositions HW: p.358 #67-87

More Related