4-2 inverse functions. * right answer : d graph and recognize inverses of relations and functions....
TRANSCRIPT
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4-2 Inverse Functions
*CHAPTER 4
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*SAT problem of the day
*If &y=, then which of the following equals &(y+6)
*A)
*B)
*C)
*D)
*E)
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*SAT Solution
*Right Answer : D
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*Objectives
Graph and recognize inverses of relations and functions.
Find inverses of functions.
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*Inverse
*You have seen the word inverse used in various ways.
* The additive inverse of 3 is –3.
*The multiplicative inverse matrix
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*Example#1
*Graph the relation and connect the points. Then graph the inverse. Identify the domain and range of each relation.
x 2 5 6 9
y 0 1 5 8
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*solution
Domain:{x|2 ≤ x ≤ 9} Range :{y|0 ≤ x ≤ 8}
Domain:{x|0 ≤ x ≤ 8} Range :{y|2 ≤ x ≤ 9}
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*Example
*Graph the relation and connect the points. Then graph the inverse. Identify the domain and range of each relation.
x 1 3 4 5 6
y 0 1 2 3 5
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*Student guided practice
*Do problems 2 and 3 in your book page 245
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*Inverse functions
*When the relation is also a function, you can write the inverse of the function f(x) as f–1(x). This notation does not indicate a reciprocal.
*Functions that undo each other are inverse functions
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*Inverse
*To find the inverse function, use the inverse operation. In the example above, 6 is added to x in f(x), so 6 is subtracted to find f–1(x).
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*Example#3
*Use inverse operations to write the inverse of
*f(x) = x – 1/2 if possible.
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*Example#4
*Use inverse operations to write the inverse of f(x) = 3(x – 7).
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*Example#5
*Use inverse operations to write the inverse of
*f(x) = x/3
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*Example
*Use inverse operations to write the inverse of f(x) = 5x – 7.
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*Student guided practice
*Do problems 4- 8 in your book page 245
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*Example
*Graph f(x) = – 1/2 x – 5. Then write the inverse and graph.
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*Graph f(x) = 2/3x + 2. Then write the inverse and graph.
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*Application
*Juan buys a CD online for 20% off the list price. He has to pay $2.50 for shipping. The total charge is $13.70. What is the list price of the CD?
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*video
*Lets watch a video
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*Homework
*Do problems 18-25 in your book page 245 and 246
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*Closure
*Today we learned about inverse functions
*Next class we are going to learn about logarithmic functions