1. Operations of Functions
SECTION 6.3
Revised ©2014
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6.3 - Function Operations
6.2 function operations

2. Operations with Functions
To add/subtract functions, COMBINE LIKE TERMS
To multiply functions and divide functions, DISTRIBUTE properly with EXPONENTS
The domain for +/–/× will be the same but division may be different.
Add or Subtract: f(x) + g(x) or (f + g)(x)
Multiply: f(x) • g(x) or (f g)(x)
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6.3 - Function Operations

3. Example 1
If given f(x)= 4x1/2 and g(x)= –9x1/2, solve (f + g)(x). Leave answer in exponential form.
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6.3 - Function Operations

4. Example 2
If given f(x) = 6x and g(x) = x3/4, solve (fg)(x). Leave answer in exponential form.
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6.3 - Function Operations

5. Your Turn If given f(x)= 3x2 + x and g(x)= 4x – 2, solve (f – g)(x).
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6.3 - Function Operations

6. Compositions Determine what is substituted
Take the INSIDE function and replace it
Take the outside function and bring it down
Replace the variable with the leftover variable
Simplify the expression
Notation: They may give you f(g(x)) or 𝒇∘𝒈 𝒙. The meaning is the same.
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6.3 - Function Operations

7. Written Notation It may be written as… It may not be written as:
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6.3 - Function Operations

8. Example 3 If given f(x) = 4x and g(x) = 2 – x, solve f(g(x))
6.3 - Function Operations

9. Example 4 If given f(x) = 4x and g(x) = 2 – x, solve 𝒈∘𝒇 𝒙
6.3 - Function Operations

10. Example 5 If given f(x) = 4x and g(x) = 2 – x, solve g(f(f(x)))
6.3 - Function Operations

11. Your Turn If given f(x) = 4x and g(x) = 2 – x, solve g(g(x))
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6.3 - Function Operations

12. Example 6 If given f(x) = 4x–1 and g(x) = 2 – x, solve g(f(2))
6.3 - Function Operations

13. Example 7 If given f(x) = 4x–1 and g(x) = 2 – x, solve 𝒇∘𝒈 (𝟓)
6.3 - Function Operations

14. Example 7 If given f(x) = 4x–1 and g(x) = 2 – x, solve f(g(y))
6.3 - Function Operations

15. Example 8 If given f(x) = x2 + 2x – 1 and 𝒈 𝒙 = 𝟏 𝒙−𝟑 , solve 𝒇∘𝒈 (𝒙)
6.3 - Function Operations

16. Your Turn If given f(x) = x2 + 2x – 1 and 𝒈 𝒙 = 𝟏 𝒙−𝟑 , solve 𝒈∘𝒇 (𝒙)
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6.3 - Function Operations

17. Example 9
You have a $10 gift card to a paint store. The store is offering 15% off your entire purchase of any paints and painting supplies. You decide to purchase a $30 can of paint and $25 worth of painting supplies. You have the option to use the gift card or the discount first. Which one should you first? Justify your reasoning.
Total amount of paying for paint:
Function for the $10 gift card:
Function for the 15% discount:
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6.3 - Function Operations

18. Example 9
You have a $10 gift card to a paint store. The store is offering 15% off your entire purchase of any paints and painting supplies. You decide to purchase a $30 can of paint and $25 worth of painting supplies. You have the option to use the gift card or the discount first. Which one should you first? Justify your reasoning.
Use the 15% discount first: Use the Gift Card first:
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6.3 - Function Operations

19. Assignment
Worksheet on Synthetic Division and complete WKST on Function Operations
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6.3 - Function Operations