Download presentation

1
**Combinations of Functions**

Section 1.4

2
**Sum, Difference, Product, & Quotient of Functions**

Let f & g be 2 functions with overlapping domains. then, for all x common to both domains, the sum, difference, product, and quotient of f & g are defined as: 1. Sum ( f+g )(x) = f (x) + g (x) 2. Difference ( f - g )(x) = f (x) - g (x) 3. Product ( f • g )(x) = f (x) • g (x) 4. Quotient ( f / g )(x) = f (x) / g (x), g(x) ≠ 0

3
**Example 1 Given f(x) = 2x + 1 & g(x) = x2 + 2x - 1**

Find the sum and difference of the functions. ( f + g)(x) = f(x) + g(x) = (2x+1) + (x2 + 2x - 1) = x2 + 4x ( f - g)(x) = f(x) - g(x) = (2x+1) - (x2 + 2x - 1) = -x2 + 2

4
**Example 1 cont... Find the product of the functions.**

Given f(x) = 2x + 1 & g(x) = x2 + 2x - 1 Find the product of the functions.

5
**Example 2 Given f(x) = x + 1 & g(x) = x2 - 2x - 3**

Find the quotient of the functions. The domain of g(x) is all #’s except 3, Even though it is canceled, this is still the domain.

6
**Example 2 Given & Find the quotient of the functions.**

The domain of f(x) is all #’s except -1. Even though we canceled, this is still the domain.

7
**You Try Given f(x) = 3x - 2 & g(x) = 3x2 + x - 2**

Find the sum and difference of the functions. ( f + g)(x) = f(x) + g(x) = (3x - 2) + (3x2 + x - 2) = 3x2 + 4x - 4 ( f - g)(x) = f(x) - g(x) = (3x - 2) - (3x2 + x - 2) = -3x2 + 2x

8
**You Try Given f(x) = 3x - 2 & g(x) = 3x2 + x - 2**

Find the product & quotient of the functions. ( f • g)(x) = f(x) • g(x) = (3x - 2)(3x2 + x - 2) = 9x3 -3x2 -8x + 4 (f ÷ g)(x) = f(x)/g(x) = (3x-2)/(3x2 + x - 2) = 1/(x+1) The domain is still x ≠ 2/3, -1

9
**Composition of Functions**

Definition of The Composition of Two Functions. The composition of the function f with the function g is (f∘g)(x) The domain of (f∘g)(x) is the set of all x in the domain of g such that g(x) is in the domain of f.

10
**Example 3 Given f(x) = x + 2 & g(x) = 4- x2, find the following.**

a) f(g(x)) = (4- x2) + 2 = 6 - x2 This means go to the f function and replace x with the g function.

11
**Example 3 Given f(x) = x + 2 and g(x) = 4 - x2, find the following.**

a) (g ∘f)(x) This means go to the g function and replace x with the f function. g(f(x)) = 4 - (x + 2)2 = 4-(x2 + 4x + 4) = -x2 - 4x

12
Example 4 cont.. Given f(x) = x + 2 and g(x) = 4 - x2, find the following. b) (g ∘f)(-2) This means go to the f function & replace x with -2. Take that answer & put it into g. f(-2) = = 0 g(0) = = 4

13
Example 4 cont.. Given f(x) = x + 2 and g(x) = 4 - x2, find the following. b) (g ∘f)(-2) You could also go to your answer for (g ∘f)(x) & replace x with a -2 g( f(x)) =-x2 - 4x = -(-2)2 - 4(-2) = 4

14
**You Try Given f(x) = x - 2 & g(x) = x2 + 2x, find the following.**

a) (f∘g)(x) (x2 + 2x) - 2 = x2 + 2x - 2 b) (g ∘f)(x) (x - 2)2 + 2(x - 2) = x2 - 2x c) (f∘g)(2) (2)2 + 2(2) - 2 = 6 d) (g∘f)(3) (3)2 - 2(3) = 3

15
**Finding the Domain of the Composition of Functions**

Given f(x) = x2 - 9 & g(x) = √(9-x2), find the composition f(g(x)). Then find the domain of f(g(x)). We take the f function & replace x with the g function. f(g(x)) = ((√ 9-x2))2 - 9 = 9 - x2 - 9 = -x2

16
Example 5 So the composition f(g(x)) = x2, and the domain of this function is all real numbers. However, this is not the domain of the composition. We need to look at the domain of g(x) to know the domain of the composition. g(x) = √(9-x2), so its domain is where 9 - x2 ≥ 0 g(x) = √(9-x2) x2 ≥ 0 [-3, 3]

Similar presentations

Presentation is loading. Please wait....

OK

Continuity Section 2.3a.

Continuity Section 2.3a.

© 2018 SlidePlayer.com Inc.

All rights reserved.

To ensure the functioning of the site, we use **cookies**. We share information about your activities on the site with our partners and Google partners: social networks and companies engaged in advertising and web analytics. For more information, see the Privacy Policy and Google Privacy & Terms.
Your consent to our cookies if you continue to use this website.

Ads by Google

Ppt on gadgets used at home Ppt on cultural heritage of india Ppt on eisenmenger syndrome in adults Ppt on nitrogen cycle and nitrogen fixation is carried Ppt on bond length and energy Dot matrix display ppt online Ppt on summary writing practice Ppt on indian army weapons purchase Ppt on social networking in our lives Ppt on big dig collapse