Download presentation

Presentation is loading. Please wait.

Published byAmelia Orr Modified over 2 years ago

1
One-to-One Functions; Inverse Function

2
A function f is one-to-one if for each x in the domain of f there is exactly one y in the range and no y in the range is the image of more than one x in the domain. A function is not one-to-one if two different elements in the domain correspond to the same element in the range.

3
x1x1 x2x2 x3x3 y1y1 y2y2 y3y3 x1x1 x3x3 y1y1 y2y2 y3y3 x1x1 x2x2 x3x3 y1y1 y3y3 Domain Range One-to-one function Not a function NOT One-to-one function

4
M : Mother Function is NOT one-one Joe Samantha Anna Ian Chelsea George Laura Julie Hilary Barbara Sue HumansMothers

5
S: Social Security function IS one-one Joe Samantha Anna Ian Chelsea George AmericansSSN

6
Is the function f below one – one?

7
Theorem Horizontal Line Test If horizontal lines intersect the graph of a function f in at most one point, then f is one-to-one.

8
Use the graph to determine whether the function is one-to-one. Not one-to-one.

9
Use the graph to determine whether the function is one-to-one. One-to-one.

10
The inverse of a one-one function is obtained by switching the role of x and y

11
SSN Joe Samantha Anna Ian Chelsea George Americans The inverse of the social security function

12
Let and Find

13
g is the inverse of f.

14
. Let f denote a one-to-one function y = f(x). The inverse of f, denoted by f -1, is a function such that f -1 (f( x )) = x for every x in the domain of f and f(f -1 (x))=x for every x in the domain of f -1.

15
Domain of fRange of f

16
Theorem The graph of a function f and the graph of its inverse are symmetric with respect to the line y = x.

17
y = x (2, 0) (0, 2)

18
Finding the inverse of a 1-1 function Step1: Write the equation in the form Step2: Interchange x and y. Step 3: Solve for y. Step 4: Write for y.

19
Find the inverse of Step1: Step2: Interchange x and y Step 3: Solve for y

20

21

22

Similar presentations

© 2016 SlidePlayer.com Inc.

All rights reserved.

Ads by Google