Composite and Inverse Functions

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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

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 mowerA = f(s)
• The time required to mow is a function of square yds/hr you cover T = g(A)
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 Functions
• Given
• Find the following compositions

Try using your calculator

1

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

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 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
• 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
• 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
• 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
• 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
• 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

Assignment
• Lesson 2.4
• Page 82
• Exercises1 – 37 odd