Download presentation

Published bySusanna Arnold Modified over 4 years ago

1
Combinations of Functions & Inverse Functions Obj: Be able to work with combinations/compositions of functions. Be able to find inverse functions. TS: Making decisions after reflections and review Warm-Up: Given f(x) = 2x + 3 and g(x) = x2 – 4, find… f(2) + g(2) g(3) – f(3)

2
**Arithmetic Combinations**

Where the domain is the real numbers that both f and g’s domains have in common. For f/g also g(x) ≠ 0.

3
**Examples Find each of the below combinations given**

(f∙g)(2) ) (f/g)(x) & its domain (f – g)(2)

4
**Arithmetic Compositions (f○g)(x) = f(g(x))**

Given the below find each of the following. (f ○ g)(2) ) g(f(-1))

5
**Arithmetic Compositions (f○g)(x) = f(g(x))**

Given the below find each of the following. 3) f(g(x)) & its domain

6
**Find f(g(x)) and g(f(x))**

7
**Definition of the Inverse of a Function**

Let f and g be two functions where f(g(x)) = x for every x in the domain of g, and g(f(x)) = x for every x in the domain of f. Under these conditions, g is the inverse of f and g is denoted f-1. Thus f(f-1(x))=x and f-1(f(x))=x where the domain of f must equal the range of f-1 and the range of f must equal the domain of f-1.

8
Graphs of Inverses Two equations are inverses if their graphs are reflections of one another across the line y=x. y f y=x f -1 1 x 1

9
Inverse FUNCTIONS A function f(x) has an inverse function if the graph of f(x) passes the ___________________. (In other words the relation is ONE-TO-ONE: For each y there is exactly one x) Circle the functions that are one-to-one (aka have inverse functions) y y y y x x x x y x

10
Examples: Determine if the two functions f and g are inverses. 1) and

11
Finding an Inverse Verify that the function is one-to-one thus has an inverse function using the Horizontal Line Test. Switch x & y. Solve for y. Make sure to use proper inverse notation for y for your final answer. (Ex: f-1(x), not y) To check your answer: Verify they are inverses by testing to see if f(f-1(x)) = f-1(f(x)) = x

12
Find the inverse function if there is one, if there is not one, restrict the domain to make it one-to-one then find the inverse function . f(x) = -.5x + 3

13
Find the inverse function if there is one, if there is not one, restrict the domain to make it one-to-one then find the inverse function . 2) f(x) = x2 – 4

Similar presentations

© 2020 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google