1 / 11

Chapter 5 Inverse Functions and Applications Section 5.3

Chapter 5 Inverse Functions and Applications Section 5.3. Section 5.3 Determining the Inverse Using Composition of Functions. Using Composition to Verify Inverse Functions Applications. Inverse Functions Two functions f and g are inverses of each other if and only if:

reillyr
Download Presentation

Chapter 5 Inverse Functions and Applications Section 5.3

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. Chapter 5 Inverse Functions and ApplicationsSection 5.3

  2. Section 5.3Determining the Inverse Using Composition of Functions • Using Composition to Verify Inverse Functions • Applications

  3. Inverse Functions Two functions f and g are inverses of each other if and only if: (f ◦ g)(x) = f(g(x)) = x for every x in the domain of g and (g ◦ f)(x) = g(f(x)) = x for every x in the domain of f. So, and . The domain of f is equivalent to the range of g and vice versa.

  4. Determine whether the given functions f and g are inverses of each other. If g(x) is the inverse of f(x), then (f ◦ g)(x) = x. It checks. If f(x) is the inverse of g(x), then (g ◦ f)(x) = x. It checks. Therefore, f and g are inverses of each other.

  5. Determine whether the given functions f and g are inverses of each other. Let us find f ◦ g. Since f ◦ g  x, there is no need to find g ◦ f. Functions f and g are not inverses of each other. Note: Recall from Section 5.1 that f-1(x) is the notation for the inverse function and it does not mean the reciprocal of f(x). That is,

  6. Find the inverse function of for x  0. Verify algebraically and graphically that f and f-1(x) are inverses of each other. The inverse is: Verifying: (continued on the next slide)

  7. (Contd.) The graphs of f and f-1(x) for the specified domain are shown next. Observe that the graphs of the functions are symmetric with respect to y = x.

  8. As of 2014, the sales tax rate in Tallahassee, Florida was one of the highest, at 7.5%. Source: www.sale-tax.com/Florida • If the function T(p)= 0.075p represents the sales tax in • Tallahassee, Florida for price p, determine T-1(p) and explain its meaning in the context of this problem. • Theinverseis: • The inverse gives the price of an item or service if p dollars are paid as sales tax. • (continued on the next slide)

  9. (Contd.) b. Evaluate and interpret T-1(18.75). We know: If the sales tax is $18.75, the price is $250. (continued on the next slide)

  10. (Contd.) c. Show that T and T-1 are inverses of each other. Since the result is p for both compositions, T and T-1 are inverses of each other.

  11. Using your textbook, practice the problems assigned by your instructor to review the concepts from Section 5.3.

More Related