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![Page 1: Operations with Functions Objective: Perform operations with functions and find the composition of two functions.](https://reader035.fdocuments.in/reader035/viewer/2022062511/5513faee550346d8488b4610/html5/thumbnails/1.jpg)
Operations with Functions
Objective: Perform operations with functions and find the composition of
two functions
![Page 2: Operations with Functions Objective: Perform operations with functions and find the composition of two functions.](https://reader035.fdocuments.in/reader035/viewer/2022062511/5513faee550346d8488b4610/html5/thumbnails/2.jpg)
![Page 3: Operations with Functions Objective: Perform operations with functions and find the composition of two functions.](https://reader035.fdocuments.in/reader035/viewer/2022062511/5513faee550346d8488b4610/html5/thumbnails/3.jpg)
32 x 10x 62 xx
x5 xx 39 2
![Page 4: Operations with Functions Objective: Perform operations with functions and find the composition of two functions.](https://reader035.fdocuments.in/reader035/viewer/2022062511/5513faee550346d8488b4610/html5/thumbnails/4.jpg)
Operations with Functions
• For all functions f and g:
• Sum: (f + g)(x) = f(x) + g(x)• Difference (f – g)(x) = f(x) – g(x)• Product (fg)(x) = f(x)g(x)• Quotient (f/g)(x) = f(x)/g(x)
![Page 5: Operations with Functions Objective: Perform operations with functions and find the composition of two functions.](https://reader035.fdocuments.in/reader035/viewer/2022062511/5513faee550346d8488b4610/html5/thumbnails/5.jpg)
Example 1
![Page 6: Operations with Functions Objective: Perform operations with functions and find the composition of two functions.](https://reader035.fdocuments.in/reader035/viewer/2022062511/5513faee550346d8488b4610/html5/thumbnails/6.jpg)
Example 1
![Page 7: Operations with Functions Objective: Perform operations with functions and find the composition of two functions.](https://reader035.fdocuments.in/reader035/viewer/2022062511/5513faee550346d8488b4610/html5/thumbnails/7.jpg)
Example 1
![Page 8: Operations with Functions Objective: Perform operations with functions and find the composition of two functions.](https://reader035.fdocuments.in/reader035/viewer/2022062511/5513faee550346d8488b4610/html5/thumbnails/8.jpg)
Try This
• Let and .• Find: (f + g)(x) (f – g)(x)
5.2127)( 2 xxxf 57)( 2 xxg
![Page 9: Operations with Functions Objective: Perform operations with functions and find the composition of two functions.](https://reader035.fdocuments.in/reader035/viewer/2022062511/5513faee550346d8488b4610/html5/thumbnails/9.jpg)
Try This
• Let and .• Find: (f + g)(x) (f – g)(x)
5.2127)( 2 xxxf 57)( 2 xxg
)57()5.2127())(( 22 xxxxgf
5.212 x
![Page 10: Operations with Functions Objective: Perform operations with functions and find the composition of two functions.](https://reader035.fdocuments.in/reader035/viewer/2022062511/5513faee550346d8488b4610/html5/thumbnails/10.jpg)
Try This
• Let and .• Find: (f + g)(x) (f – g)(x)
5.2127)( 2 xxxf 57)( 2 xxg
)57()5.2127())(( 22 xxxxgf
5.212 x
)57()5.2127())(( 22 xxxxgf
5.71214 2 xx
![Page 11: Operations with Functions Objective: Perform operations with functions and find the composition of two functions.](https://reader035.fdocuments.in/reader035/viewer/2022062511/5513faee550346d8488b4610/html5/thumbnails/11.jpg)
Example 2
![Page 12: Operations with Functions Objective: Perform operations with functions and find the composition of two functions.](https://reader035.fdocuments.in/reader035/viewer/2022062511/5513faee550346d8488b4610/html5/thumbnails/12.jpg)
Example 2
![Page 13: Operations with Functions Objective: Perform operations with functions and find the composition of two functions.](https://reader035.fdocuments.in/reader035/viewer/2022062511/5513faee550346d8488b4610/html5/thumbnails/13.jpg)
Example 2
![Page 14: Operations with Functions Objective: Perform operations with functions and find the composition of two functions.](https://reader035.fdocuments.in/reader035/viewer/2022062511/5513faee550346d8488b4610/html5/thumbnails/14.jpg)
Try This
• Let and .• Find: (f g)(x) (f/g)(x)
13)( 2 xxf 2)( xxg
![Page 15: Operations with Functions Objective: Perform operations with functions and find the composition of two functions.](https://reader035.fdocuments.in/reader035/viewer/2022062511/5513faee550346d8488b4610/html5/thumbnails/15.jpg)
Try This
• Let and .• Find: (f g)(x) (f/g)(x)
13)( 2 xxf 2)( xxg
263)2)(13())(( 232 xxxxxxfg
![Page 16: Operations with Functions Objective: Perform operations with functions and find the composition of two functions.](https://reader035.fdocuments.in/reader035/viewer/2022062511/5513faee550346d8488b4610/html5/thumbnails/16.jpg)
Try This
• Let and .• Find: (f g)(x) (f/g)(x)
13)( 2 xxf 2)( xxg
263)2)(13())(( 232 xxxxxxfg
2;2
13))(/(
2
xx
xxgf
![Page 17: Operations with Functions Objective: Perform operations with functions and find the composition of two functions.](https://reader035.fdocuments.in/reader035/viewer/2022062511/5513faee550346d8488b4610/html5/thumbnails/17.jpg)
![Page 18: Operations with Functions Objective: Perform operations with functions and find the composition of two functions.](https://reader035.fdocuments.in/reader035/viewer/2022062511/5513faee550346d8488b4610/html5/thumbnails/18.jpg)
Example 3
![Page 19: Operations with Functions Objective: Perform operations with functions and find the composition of two functions.](https://reader035.fdocuments.in/reader035/viewer/2022062511/5513faee550346d8488b4610/html5/thumbnails/19.jpg)
Example 3
![Page 20: Operations with Functions Objective: Perform operations with functions and find the composition of two functions.](https://reader035.fdocuments.in/reader035/viewer/2022062511/5513faee550346d8488b4610/html5/thumbnails/20.jpg)
Example 3
![Page 21: Operations with Functions Objective: Perform operations with functions and find the composition of two functions.](https://reader035.fdocuments.in/reader035/viewer/2022062511/5513faee550346d8488b4610/html5/thumbnails/21.jpg)
Try This
• Let and .• Find: and
32)( 2 xxf xxg 2)(
gf fg
![Page 22: Operations with Functions Objective: Perform operations with functions and find the composition of two functions.](https://reader035.fdocuments.in/reader035/viewer/2022062511/5513faee550346d8488b4610/html5/thumbnails/22.jpg)
Try This
• Let and .• Find: and
32)( 2 xxf xxg 2)(
gf fg
383)2(2)2( 22 xxxfgf
![Page 23: Operations with Functions Objective: Perform operations with functions and find the composition of two functions.](https://reader035.fdocuments.in/reader035/viewer/2022062511/5513faee550346d8488b4610/html5/thumbnails/23.jpg)
Try This
• Let and .• Find: and
32)( 2 xxf xxg 2)(
gf fg
383)2(2)2( 22 xxxfgf
64)32(2)32( 222 xxxgfg
![Page 24: Operations with Functions Objective: Perform operations with functions and find the composition of two functions.](https://reader035.fdocuments.in/reader035/viewer/2022062511/5513faee550346d8488b4610/html5/thumbnails/24.jpg)
Example 4
![Page 25: Operations with Functions Objective: Perform operations with functions and find the composition of two functions.](https://reader035.fdocuments.in/reader035/viewer/2022062511/5513faee550346d8488b4610/html5/thumbnails/25.jpg)
Example 4
![Page 26: Operations with Functions Objective: Perform operations with functions and find the composition of two functions.](https://reader035.fdocuments.in/reader035/viewer/2022062511/5513faee550346d8488b4610/html5/thumbnails/26.jpg)
Example 4
![Page 27: Operations with Functions Objective: Perform operations with functions and find the composition of two functions.](https://reader035.fdocuments.in/reader035/viewer/2022062511/5513faee550346d8488b4610/html5/thumbnails/27.jpg)
Example 5
• Let and . • Find
43)( xxf 2)( xxg
)3)(( gf
![Page 28: Operations with Functions Objective: Perform operations with functions and find the composition of two functions.](https://reader035.fdocuments.in/reader035/viewer/2022062511/5513faee550346d8488b4610/html5/thumbnails/28.jpg)
Example 5
• Let and . • Find• You have two choices. • First, let’s find f(g(x)) and evaluate it at x = 3.
43)( xxf 2)( xxg
)3)(( gf
![Page 29: Operations with Functions Objective: Perform operations with functions and find the composition of two functions.](https://reader035.fdocuments.in/reader035/viewer/2022062511/5513faee550346d8488b4610/html5/thumbnails/29.jpg)
Example 5
• Let and . • Find• You have two choices. • First, let’s find f(g(x)) and evaluate it at x = 3.
43)( xxf 2)( xxg
)3)(( gf
43))(( 2 xxgf
314)3(3))3(( 2 gf
![Page 30: Operations with Functions Objective: Perform operations with functions and find the composition of two functions.](https://reader035.fdocuments.in/reader035/viewer/2022062511/5513faee550346d8488b4610/html5/thumbnails/30.jpg)
Example 5
• Let and . • Find• You have two choices. • Second, we can find g(3) and put that answer into f.
43)( xxf 2)( xxg
)3)(( gf
![Page 31: Operations with Functions Objective: Perform operations with functions and find the composition of two functions.](https://reader035.fdocuments.in/reader035/viewer/2022062511/5513faee550346d8488b4610/html5/thumbnails/31.jpg)
Example 5
• Let and . • Find• You have two choices. • Second, we can find g(3) and put that answer into f.
43)( xxf 2)( xxg
)3)(( gf
9)3( g
314)9(3)9( f
![Page 32: Operations with Functions Objective: Perform operations with functions and find the composition of two functions.](https://reader035.fdocuments.in/reader035/viewer/2022062511/5513faee550346d8488b4610/html5/thumbnails/32.jpg)
![Page 33: Operations with Functions Objective: Perform operations with functions and find the composition of two functions.](https://reader035.fdocuments.in/reader035/viewer/2022062511/5513faee550346d8488b4610/html5/thumbnails/33.jpg)
Homework
• Page 115• 11-55 odd