Operations of Functions SECTION 6.3 ©2012, vdang@houstonisd.org 1/1/2019 3:31 AM 6.3 - Function Operations 6.2 function operations

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. 1/1/2019 3:31 AM 6.3 - Function Operations 6.2 function operations

Example 1 If given f(x)= 4x1/2 and g(x)= –9x1/2, solve (f + g)(x). Leave answer in exponential form. 1/1/2019 3:31 AM 6.3 - Function Operations 6.2 function operations

Your Turn If given f(x)= 3x2 + x and g(x)= 4x – 2, solve (f – g)(x). 1/1/2019 3:31 AM 6.3 - Function Operations 6.2 function operations

Example 2 If given f(x) = 6x and g(x) = x3/4, solve (fg)(x). Leave answer in exponential form. 1/1/2019 3:31 AM 6.3 - Function Operations 6.2 function operations

Your Turn If given and , solve 6.2 function operations 1/1/2019 3:31 AM 6.3 - Function Operations 6.2 function operations

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. 1/1/2019 3:31 AM 6.3 - Function Operations 6.2 function operations

Written Notation It may be written as… It is NOT known as… 1/1/2019 3:31 AM 6.3 - Function Operations 6.2 function operations

Example 3 If given f(x) = 4x and g(x) = 2 – x, solve f(g(x)) 6.3 - Function Operations 6.2 function operations

Example 4 If given f(x)= 4x and g(x)= 2 – x, solve g(f(x)) 6.3 - Function Operations 6.2 function operations

Example 5 If given f(x) = 4x and g(x) = 2 – x, solve g(f(f(x))) 6.3 - Function Operations 6.2 function operations

Your Turn If given f(x) = 4x and g(x) = 2 – x, solve g(g(x)) 1/1/2019 3:31 AM 6.3 - Function Operations 6.2 function operations

Example 6 If given f(x) = 4x–1 and g(x) = 2 – x, solve g(f(2)) 6.3 - Function Operations 6.2 function operations

Example 7 If given f(x) = 4x–1 and g(x) = 2 – x, solve f(g(5)) 6.3 - Function Operations 6.2 function operations

Your Turn If given f(x) = 4x–1 and g(x) = 2 – x, solve f(g(y)) 1/1/2019 3:31 AM 6.3 - Function Operations 6.2 function operations

Example 8 If given and , solve 6.2 function operations

Example 9 If given and , solve 6.2 function operations

Your Turn If given and , solve 6.2 function operations 1/1/2019 3:31 AM 6.3 - Function Operations 6.2 function operations

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: 1/1/2019 3:31 AM 6.3 - Function Operations 6.2 function operations

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: 1/1/2019 3:31 AM 6.3 - Function Operations 6.2 function operations

Assignment Page 432 3-19 EOO, 21-37 odd, 45; no need to label domain 1/1/2019 3:31 AM 6.3 - Function Operations 6.2 function operations