Download presentation

1
**Composition of Functions**

Pg. 60 – 61 February 17, 2015

2
**Warm-Up 1) Find the inverse function of y = –3x – 6**

Simplify the expression… ½ (2x + 4) – 2

3
Title Composition of Functions In the composition function f(g(x)), the ________ of g(x) is used as the ________ of the function f(x). In the composition g(f(x)), the _______ of f(x) is used as the _______ of g(x). NOTE: f(g(x)) can also be written as (f ᵒ g)(x)

4
**What is function composition ?**

Essential Question What is function composition ?

5
What is it? A composition of two functions uses one function as the INPUT for the other function. It is written as either f(g(x)) or as f◦g(x). Both mean to use the “g” function as the input for the “f” function. So, the expression for “g” replaces the x in function “f.” It reads as “the f of g of x”

6
*NOTE* g(f(x)) & g◦f(x) mean to use the “f” as the input. It is read as “the g of f of x.” Performing a composition with values: If f(x) = 3x – 11 and g(x) = 4x + 7, find the f(g(6)). Work from inside-out: f(4(6)+7) = f(31) = 3(31) – 11 = 93 – 11 = 82 …PLUG 6 INTO g(x) and SIMPLIFY… NOW USE that value as the INPUT for “f” and SIMPLIFY

7
**Find the composition function… g(f(x)) when f(x) = 3x – 11 and g(x) = 4x + 7.**

f(g(x)) = f (4x + 7) … use function “g” as your INPUT = 3( ) – 11 … it plugs INTO function “f” = 3(4x + 7) – 11 … simplify to find the composite function = 12x + 21 – 11 = x + 10 find the g(f(x)) = g(3x – 11 )… now “f” is the INPUT = 4(3x – 11) + 7 … plug into “g” = 12x – … simplify = 12x – 37

8
Example 3 Find the f◦g(x) when f(x) = 2/3 x – 5 and g(x) = 6x – 18. f(g(x)) = f(6x – 18) = (2/3)(6x – 18) – 5 = 4x – 12 – 5 = 4x – 17 Find the g◦f(x): g(f(x)) = g(2/3 x – 5) = 6(2/3 x – 5) – 18 = 4x – 30 – 18 = 4x - 48

9
Example 4 Find the f◦g(x) when f(x) = x2 + 3 and g(x) = 2x – 1. f(g(x)) = f(2x – 1) = (2x – 1)2 + 3 = (2x – 1)(2x – 1) + 3 = 4x2 – 4x = 4x2 – 4x + 4 Find the g◦f(x): g(f(x)) = g(x2 + 3) = 2(x2 + 3) – 1 = 2x2 + 6 – 1 = 2x2 + 5

10
HOMEWORK Problems Given: f(x) = 4x – 8, g(x) = 2x2 – 5 & h(x) = ¼ x + 2 Find the following: f(h(3)) g(f(5)) h(g(–2)) f(g(x)) h(f(x)) h(g(x))

Similar presentations

OK

2.3 Combinations of Functions Introductory MATHEMATICAL ANALYSIS For Business, Economics, and the Life and Social Sciences (12 th Edition) Copyright ©

2.3 Combinations of Functions Introductory MATHEMATICAL ANALYSIS For Business, Economics, and the Life and Social Sciences (12 th Edition) Copyright ©

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Download ppt on oxidation and reduction calculator Ppt on plant cell structure Well made play ppt on apple Ppt on next generation 2-stroke engine diagram A ppt on spirit of unity Ppt on infrared remote control system Ppt on waxes poetic Ppt on javascript events textbox Ppt on professional development Ppt on object-oriented programming php