1. Operations of Functions
SECTION 6.3
©2012,
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2. Operations with Functions
To add/subtract functions, COMBINE LIKE TERMS
To multiply functions and divide functions, DISTRIBUTE properly with EXPONENTS
The domain for +/-/x will be the same but division may be different.
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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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4. Your Turn If given f(x)= 3x2 + x and g(x)= 4x – 2, solve (f – g)(x).
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5. 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. Your Turn If given and , solve 6.2 function operations
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7. 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 The meaning is the same.
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8. Written Notation It may be written as… It is NOT known as…
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9. Example 3 If given f(x) = 4x and g(x) = 2 – x, solve f(g(x))
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10. Example 4 If given f(x)= 4x and g(x)= 2 – x, solve g(f(x))
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11. Example 5 If given f(x) = 4x and g(x) = 2 – x, solve g(f(f(x)))
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12. Your Turn If given f(x) = 4x and g(x) = 2 – x, solve g(g(x))
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13. Example 6 If given f(x) = 4x–1 and g(x) = 2 – x, solve g(f(2))
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14. Example 7 If given f(x) = 4x–1 and g(x) = 2 – x, solve f(g(5))
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15. Your Turn If given f(x) = 4x–1 and g(x) = 2 – x, solve f(g(y))
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16. Example 8 If given and , solve 6.2 function operations

17. Example 9 If given and , solve 6.2 function operations

18. Your Turn If given and , solve 6.2 function operations
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19. Example 10
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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20. Example 10 Use the 15% discount first: Use the Gift Card first:
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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21. Assignment Page 432 3-19 EOO, 21-37 odd, 45; no need to label domain
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