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# Composite and Inverse Functions - PowerPoint PPT Presentation

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)

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

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### Composite and Inverse Functions

Lesson 2.4

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 mowerA = f(s)

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

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?

• Given

• Find the following compositions

4

3

-3

3

1

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

• 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

• 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

• 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

• Given the following table which defines the function f

• Determine

• f(-2)

• f -1(2)

• f -1(-4)

• f(-1)

• Write some ordered pairsfor the functiondefined by thisgraph

• Determinef -1(0)f -1(-2)

• Is the inverse even a function?

• Given the formula

• Find the inverse function f -1(V)

• Strategy

• Write in formula notation

• Solve for the independent variable r = ?

• 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