Composite and inverse functions
1 / 13

Composite and Inverse Functions - PowerPoint PPT Presentation

  • Uploaded on

Composite and Inverse Functions. Lesson 2.4. speed. f(s). sq yds/hr. g(A). Time. Composition of Functions. Consider two functions where the output of one is the input of the next Example Square yds/hr mowed is a function of how fast you push the mower A = f(s)

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
Download Presentation

PowerPoint Slideshow about ' Composite and Inverse Functions' - hakeem-dillon

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.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

Composition of functions



sq yds/hr



Composition of Functions

  • Consider two functions where the output of one is the input of the next

  • Example

    • Square yds/hr mowed is a function of how fast you push the mowerA = f(s)

    • The time required to mow is a function of square yds/hr you cover T = g(A)

Composition of functions1
Composition of Functions

Given the following functions

  • Q = f(p) The number of barrels of oil sold when the price is p dollars per barrel

  • R(Q) is the revenue earned when Q barrels are sold

  • What is R(f(p)) ?

    • What are the units of each function?

Composition of functions2
Composition of Functions

  • Given

  • Find the following compositions

Try using your calculator

Inverse functions







Inverse Functions

  • What if we cram a numberup the spout of a function and out of the funnel popsthe number that wouldhave given us the result??

  • The function that does this is called theinverse function

Use spreadsheet to evaluate inverse of a function

Perspectives for input and output
Perspectives for Input and Output

  • Suppose you are told 1 gallon of paint covers 250 ft2

    • You might derive the function

  • It is just as reasonable to consider how many gallons are needed for a certain area

Perspectives for input and output1
Perspectives for Input and Output

  • The mathematical relationship is the same

    • The input on one f(g) is the output on h(A)

  • We would say the functions have an inverse relationship

Inverse function notation
Inverse Function Notation

  • For the inverse of function f, we use the notation f -1

  • Note that this is not the same as a negative exponent

    • It is not

Finding inverse values from a table
Finding Inverse Values from a Table

  • Given the following table which defines the function f

  • Determine

    • f(-2)

    • f -1(2)

    • f -1(-4)

    • f(-1)

Finding inverse values from a graph
Finding Inverse Values from a Graph

  • Write some ordered pairsfor the functiondefined by thisgraph

  • Determinef -1(0)f -1(-2)

  • Are there multiple answers

  • Is the inverse even a function?

Finding the inverse formula
Finding the Inverse Formula

  • Given the formula

  • Find the inverse function f -1(V)

  • Strategy

    • Write in formula notation

    • Solve for the independent variable r = ?

Domain and range of an inverse function
Domain and Range of An Inverse Function

  • Note that the domain of the original function becomes the range of the inverse

    • Thus restrictions on the original domain affect the range of the inverse

  • AlsoThe range of the original may be restricted

    • This affects the domain of the inverse

  • Consider the inverses of these functions

As we saw on slide 10, some inverses might not even be functions


  • Lesson 2.4

  • Page 82

  • Exercises1 – 37 odd