1 / 9

6.4 “Inverse Functions”

6.4 “Inverse Functions”. A relation is a pairing of input and output values. An inverse relation means that the domain and range are interchanged . The graph of an inverse is a reflection of the original graph. Functions f and g are inverses of each other if…..

yovela
Télécharger la présentation

6.4 “Inverse 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. 6.4 “Inverse Functions” A relation is a pairing of input and output values. An inverserelation means that the domain and range are interchanged. The graph of an inverse is a reflection of the original graph Functions f and g are inverses of each other if….. f(g(x)) = x andg(f(x)) = x The function g is written as f-1(x), which is the inverse.

  2. Finding Equations of Inverses 1. Find an equation for the inverse of y = 3x - 5 Steps: 1. Write the original problem. • Switch x and y. • Solve for y. • This is the inverse function.

  3. Verifying Inverse Functions 2. Verify that f(x) = 3x – 5 and f-1(x) = x + are inverse functions.

  4. Try These 1. Find the inverse of the function y = 4x + 2 2. Verify they are inverses.

  5. Inverses of Nonlinear Functions • Find the inverse of f(x) = x2, x ≥ 0. Then graph f(x) and f-1(x).

  6. Inverses of Nonlinear Functions 4. Consider the inverse of f(x) = 2x3 + 1. Determine whether the inverse of f is a function.

  7. Try This… 5. Find the inverse of f(x) = x2 + 2, x ≥ 0. Then graph f(x) and f-1(x).

  8. Try This Too  6. Consider the inverse of f(x) = 3x3– 4. Determine whether the inverse of f is a function.

  9. Horizontal Line Test Use the horizontal line test to see if inverses are functions. No horizontal line intersects the inverse more than once!

More Related