SAT Problem of the Day

2.4 Operations With Functions Objectives: Perform operations with functions to write new functions Find the composition of two functions

Operations With Functions For all functions f and g: (f + g)(x) = f(x) + g(x) Sum Difference (f – g)(x) = f(x) – g(x) Product (f  g)(x) = f(x)  g(x) where g(x)  0 f(x) g(x) Quotient

Example 1 Let f(x) = 4x2 + 6x – 9 and g(x) = 6x2 – x + 2. a) Find f + g. (f + g)(x) = f(x) + g(x) = (4x2 + 6x – 9) + (6x2 – x + 2) = 10x2 + 5x – 7 b) Find f - g. (f - g)(x) = f(x) - g(x) = (4x2 + 6x – 9) - (6x2 – x + 2) = -2x2 + 7x – 11

Example 2 Let f(x) = 9x2 and g(x) = 4x + 3. a) Find f · g. (f · g)(x) = f(x) · g(x) = 9x2(4x + 3) = 36x3 + 27x2 b) Find where

Practice Let f(x) = 4x2 – 2x + 1 and g(x) = -5x. Find: f + g f – g

Composition of Functions Let f and g be functions of x. The composition of f with g, denoted f ○ g, is defined by f(g(x)). The composition of g with f, denoted g ○ f, is defined by g(f(x)).

Example 3 Let f(x) = x2 + 4 and g(x) = 2x. a) Find = g(x)2 + 4 b) Find

Example 4 Let f(x) = 2x2 +3x - 5 and g(x) = 4. a) Find = 2(g(x) 2) + 3g(x) – 5 b) Find

Practice 1) Let f(x) = -2x2 + 3 and g(x) = -2x. Find

Homework Page 115 Exercises 13, 21, 30-34, 37-59 odd, 60-63

6 minutes Warm-Up (WID) Make up a word problem like the ones on the composite function worksheet. Be sure to take all the right steps: define the scenario, define your variables clearly, and then show the (composite) functions that relate the variables.