1.5 Combintions of Functions Students will be able to: - add, subtract, multiply, and divide functions. - find compositions of one function with another. - Use combinations of two functions to model and solve real-life problems.

Sum, Difference, Product, and Quotient of Function Sum: (f+g)(x) = f(x) + g(x) Difference: (f-g)(x) = f(x) – g(x) Product: (fg)(x) = f(x)•g(x) Quotient:

Example 1: Given and , find . Then evaluate the sum when x = 2.

Example 2: Given and , find (f – g)(x). Then evaluate the difference when x = 2.

Example 3 Given and , find (fg)(x). Then evaluate the product when x = 4.

Example 4: Find (f/g)(x) and (g/f)(x) for the functions given by and . Then find the domains of each.

Example 5: Find for , . If possible, find and .

Example 6: Given f(x) = x + 2 and , evaluate (a) and (b) when x = 0,1,2, and 3.

Example 7: Find the domain of the composition for the functions given by and .

Example 8: Given and , find each composition. a. b.

Example 9: Write the function as a composition of two functions.

Example 10: Write the function as a composition of two functions.

Composition of Functions: Convert miles to inches.

Example F(x) displays the percent increase in UV radiation when the ozone layer thins by x% X 1 2 3 4 5 6 F(x) 1.5 4.5 7.5 9 G(x) displays the percent increases in cases of skin cancer given the % increase in UV radiation X 1.5 3 4.5 6 7.5 9 G(x) 5.25 10.5 15.75 21.0 26.25 31.5 G(F(2) = Describe what G(F(x)) computes.