Week 4 Day 3 Composition of Functions.pptx

The ebst

1. WELCOME to our today’s session!

2. Operations on Functions        

3. The Composition of Functions g(f(x) = 0.80x – 500 = 0.80(3000) – 500 = 2400 – 500 = 1,900 f(g(x) = 0.80(x-500) = 0.80(3000 – 500) = 0.80(2500) = 2,000

4. Perform composition of functions. Objective

5. The Composition of Functions The composition of the function f with g is denoted by (f g) and is defined by the equation: (f g) (x) = f(g(x))  

6. The Composition of Functions The composition of the function g with f is denoted by (g f) and is defined by the equation: (g f) (x) = g(f(x))  

7. Given the functions: f(x) = 2x+2 & g(x) = x-1 Find (f g) (x).   (f g) (x) = f (g(x)) = 2(g(x)) + 2 = 2(x-1)+2 = _______   The Composition of Functions

8. Given the functions: f(x) = 2x+2 & g(x) = x-1 Find (f g) (x).   (f g) (x) = f (g(x)) = 2(g(x)) + 2 = 2(x-1)+2 = 2x-2+2 = 2x   The Composition of Functions

9. Given the functions: f(x) = 2x+2 & g(x) = x-1 Find (g f) (x).   (g f) (x) = g (f(x)) = (f(x)) - 1 = (2x+2)-1 = __________   The Composition of Functions

10. The Composition of Functions Given the functions: f(x) = x + 1 & g(x) = x - 5 Find (f g) (x). (f g) (x) = f(g(x)) = g(x) + 1 = (x - 5) + 1 = _______  

11. The Composition of Functions f(x) = x + 1 & g(x) = x - 5 Find (g f) (x). (g f) (x) = g(f(x)) = f(x) - 5 = (x+1) -5 = _______  

12. Given the functions: f(x) = 3x-5 and g(x) = Find (f g) (-1).   The Composition of Functions

13. Given the functions: f(x) = 3x-5 ; g(x) = and h(x) = Find (f g) (-1). (f g) (-1) = f (g(-1)) = 3( ) - 5 = 3 - 5 = 3(1) - 5 = -2   The Composition of Functions

14. Perform composition of functions. Today I learned to…

15. Given the functions: f(x) = and g(x) = Find the following: 1. 2. 3. (f g) 4. (g f)   Independent Practice