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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)

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?

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

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