Function Operations Definition Addition 1 Function operations Multiplication

Function Operations

� Definition � Addition: 1: Function operations: � Multiplication: � Subtraction: � Division:

1. Let f(x) = 3 x + 8 and g(x) = 2 x – 12. Find f + g and f – g.

Let f(x) = 5 x 2 – 4 x and g(x) = 5 x + 1. Find f + g and f – g.

Let f(x) = -2 x + 6 and g(x) = 5 x + 7. Find f + g and f – g.

4. Let f(x) = x 2 – 1 and g(x) = x + 1. Find fg and f/g.

Let f(x) = 6 x 2 + 7 x – 5 and g(x) = 2 x – 1. Find fg and f/g.

Let f(x) = x² + 1 and g(x) = x² - 1. Find f · g and f/g.

� Let f(x) = 2 x² and g(x) = 3 x – 1. Perform each function operation. �f(x) + g(x) �f(x) – g(x) �f(x)· g(x) �f(x)/g(x)

�Definition 2: Composition of Functions �The composition of function g with function f is written as g(f(x)).

7. Let f(x) = x – 2 and g(x) = x 2. Find g(f(-5)).

Find f(g(-5))

Let f(x) = x³ and g(x) = x² + 7. Find (g(f(2)).

10. Let f(x) = 3 x and g(x) = x². Find f(g(x)) and g(f(x)).

Let f(x) = x + 3 and g(x) = x – 5. Find f(g(x)) and g(f(x)).

Let f(x) = (x + 5)/2 and g(x) = x². Find f(g(x)) and g(f(x)).

� Let f(x) = 2 x² and g(x) = 3 x – 1. Perform each function operation. �f(g(-1)) �f(g(x)) �g(f(x))

� Consumer Issues: Suppose you are shopping in the store in the photo. You have a coupon worth $5 off any item. �Use functions to model discounting an item by 20% and to model applying the coupon.

�Use the composition of your two functions to model how much you would pay for an item if the clerk applies the discount first and then the coupon.

�Use the composition of your two functions to model how much you would pay for an item if the clerk applies the coupon first and then the discount.

�How much more is any time if the clerk applies the coupon first?

�A store is offering a 15% discount on all items. You have a coupon worth $2 off any item. Let x be the original cost of an item. Use a composition of functions to find a function c(x) that gives the final cost of an item if the discount is applied first and then the coupon. Then use this function to find the final cost of an item originally priced at $10.