Do Now Evaluate the function:. Homework Need help? Look in section 7.7 – Inverse Relations &...
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Transcript of Do Now Evaluate the function:. Homework Need help? Look in section 7.7 – Inverse Relations &...
![Page 1: Do Now Evaluate the function:. Homework Need help? Look in section 7.7 – Inverse Relations & Functions in your textbook Worksheet: Inverses WS.](https://reader035.fdocuments.net/reader035/viewer/2022070403/56649f315503460f94c4d1eb/html5/thumbnails/1.jpg)
Do NowEvaluate the function: 3 4g x x
1g h x
2 4h x x x
33 h x
![Page 2: Do Now Evaluate the function:. Homework Need help? Look in section 7.7 – Inverse Relations & Functions in your textbook Worksheet: Inverses WS.](https://reader035.fdocuments.net/reader035/viewer/2022070403/56649f315503460f94c4d1eb/html5/thumbnails/2.jpg)
HomeworkNeed help?
Look in section 7.7 – Inverse Relations & Functions
in your textbook
Worksheet: Inverses WS
![Page 3: Do Now Evaluate the function:. Homework Need help? Look in section 7.7 – Inverse Relations & Functions in your textbook Worksheet: Inverses WS.](https://reader035.fdocuments.net/reader035/viewer/2022070403/56649f315503460f94c4d1eb/html5/thumbnails/3.jpg)
Unit 3: Domain & RangeDay 12: Inverses
![Page 4: Do Now Evaluate the function:. Homework Need help? Look in section 7.7 – Inverse Relations & Functions in your textbook Worksheet: Inverses WS.](https://reader035.fdocuments.net/reader035/viewer/2022070403/56649f315503460f94c4d1eb/html5/thumbnails/4.jpg)
ObjectiveTo find the inverse of a relation using:
A mapping diagramA tableAn equation
To determine if an inverse relation is a function using:A mapping diagramA tableA graphAn equation
![Page 5: Do Now Evaluate the function:. Homework Need help? Look in section 7.7 – Inverse Relations & Functions in your textbook Worksheet: Inverses WS.](https://reader035.fdocuments.net/reader035/viewer/2022070403/56649f315503460f94c4d1eb/html5/thumbnails/5.jpg)
Inverse RelationsWhat is an inverse relation?
A relation that “undoes” a relation or function
The inverse of any relation is written as:
Domain (x –
values)Range
(y – values)
2 4y x x f(x)
-10
1
2
2
4
6
8
f(x) x
2
4
6
8
-10
1
2
4
2
yx
Function:
Inverse:
1f x“inverse of
f”
![Page 6: Do Now Evaluate the function:. Homework Need help? Look in section 7.7 – Inverse Relations & Functions in your textbook Worksheet: Inverses WS.](https://reader035.fdocuments.net/reader035/viewer/2022070403/56649f315503460f94c4d1eb/html5/thumbnails/6.jpg)
Inverse RelationsAnother way to think about it:
Inverses switch the domain & range of a relation
DOMAIN
RANGE-1012
2468
Relation: (-1, 2), (0, 4), (1, 6), (2, 8) Inverse: (2, -1), (4, 0), (6, 1), (8, 2) Relation
DOMAIN
RANGE
-1012
2468
Inverse
Is the relation and/or the inverse a function?
Yes, all elements in both domains correspond to one element in the range
![Page 7: Do Now Evaluate the function:. Homework Need help? Look in section 7.7 – Inverse Relations & Functions in your textbook Worksheet: Inverses WS.](https://reader035.fdocuments.net/reader035/viewer/2022070403/56649f315503460f94c4d1eb/html5/thumbnails/7.jpg)
Find the inverse of the given relation.State if the relation and/or its inverse are functions.
DOMAIN
RANGE
4 05-3
2-69
x y
3 5
-6 -3
2 1
-6 -4
Inverse: Inverse:
x y
5 3
-3 -6
1 2
-4 -6
DOMAIN
RANGE
4 05-3
2-69
FUNCTION
NOT A FUNCTION
NOT A FUNCTION
FUNCTION
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Step 3: solve for yStep 2: switch x and
y
Find the inverse of the function.
Step 1: put “y” for “f(x)”
4 8f x x 4 8y x 4 8x y 8 4x y
4
4y
8
4
x 1
24x y
1 12
4f x x Step 4: Write using
inverse notation
Determine if the inverse is a function.
Yes, the inverse is a function because all lines pass the VLT.
![Page 9: Do Now Evaluate the function:. Homework Need help? Look in section 7.7 – Inverse Relations & Functions in your textbook Worksheet: Inverses WS.](https://reader035.fdocuments.net/reader035/viewer/2022070403/56649f315503460f94c4d1eb/html5/thumbnails/9.jpg)
Inverse Relations as FunctionsIf two equations are inverses, you will be able
to apply the function, then its inverse and get back to the original value.
Find
Find
2 4f x x 1 4
2
xf x
1 6f f
6 2 6 4f 16 1 16 416
2f
6
1 2f f
3 2 3 4f 1 2 42
2f
23
Both f(g(x)) = x and g(f(x)) = x to be inverses.
![Page 10: Do Now Evaluate the function:. Homework Need help? Look in section 7.7 – Inverse Relations & Functions in your textbook Worksheet: Inverses WS.](https://reader035.fdocuments.net/reader035/viewer/2022070403/56649f315503460f94c4d1eb/html5/thumbnails/10.jpg)
Find the inverse and determine if it is a function.
Determine if the two functions are inverses.
14 2f x x
14 2y x 14 2x y
41 4
1 2x
4 8x y
1 4 8f x x
142x y
12
58
1x
g x x
f x
124 4 1g
1
1 51
8f
6
8
Choose any value for x and see if f g x x
3
4
No, the functions are not inverses.
Yes, the inverse is a function because all lines are functions.
Both f(g(x)) = x and g(f(x)) = x to be inverses.
![Page 11: Do Now Evaluate the function:. Homework Need help? Look in section 7.7 – Inverse Relations & Functions in your textbook Worksheet: Inverses WS.](https://reader035.fdocuments.net/reader035/viewer/2022070403/56649f315503460f94c4d1eb/html5/thumbnails/11.jpg)
Inverse Relations 2 4f x x
1 4
2
xf x
Function:
Inverse:
x f(x)
-1 2
0 4
1 6
2 8
x f -1(x)
2 -1
4 0
6 1
8 2
All inverses have a line of symmetry at y
= x
![Page 12: Do Now Evaluate the function:. Homework Need help? Look in section 7.7 – Inverse Relations & Functions in your textbook Worksheet: Inverses WS.](https://reader035.fdocuments.net/reader035/viewer/2022070403/56649f315503460f94c4d1eb/html5/thumbnails/12.jpg)
Determine if the graphs depict functions and their inverses.
Yes, the graphs show functions & inverses because there is a line of symmetry at y = x.
No, the graphs do not show functions & inverses because there is no line of symmetry at y = x.
![Page 13: Do Now Evaluate the function:. Homework Need help? Look in section 7.7 – Inverse Relations & Functions in your textbook Worksheet: Inverses WS.](https://reader035.fdocuments.net/reader035/viewer/2022070403/56649f315503460f94c4d1eb/html5/thumbnails/13.jpg)
Properties of InversesIf a relation maps a onto b; then an inverse
“undoes” the relation and maps b back onto a
The domain of the relation is the range of the inverse.
The range of the relation is the domain of the inverse.
Graphs of relations & inverses have a line of symmetry at the equation y = x
Domain of fRange of f
-1
Range of f
Domain of f -1
a b
f
f -1
1f f xx x
1f xf x x
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Did you meet today’s objective?What does an inverse do?Describe how to find an inverse when given:
A tableA mapping diagramA graphAn equation