Download presentation

Presentation is loading. Please wait.

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
**x1 y1 x1 y1 x2 y2 x2 x3 x3 y3 y3 One-to-one function NOT One-to-one**

Domain Range Domain Range One-to-one function NOT One-to-one function x1 y1 y2 x3 y3 Not a function Domain Range

4
**M: Mother Function is NOT one-one**

Joe Samantha Anna Ian Chelsea George Laura Julie Hilary Barbara Sue Humans Mothers

5
**S: Social Security function IS one-one**

Joe Samantha Anna Ian Chelsea George Americans SSN

6
**Is the function f below one – one?**

10 11 12 13 14 15 16 1 2 3 4 5 6 7

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.**

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

11
**The inverse of the social security function**

Joe Samantha Anna Ian Chelsea George SSN Americans

12
Let and Find

13
g is the inverse of f.

14
**Let f denote a one-to-one function y = f(x)**

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 f Range 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 (0, 2) (2, 0)

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

Similar presentations

Presentation is loading. Please wait....

OK

Functions.

Functions.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Download ppt on indus valley civilization for kids Ppt on renewable energy in india Ppt on metro bridge construction Ppt on fibonacci numbers formula Ppt on entrepreneurship development Ppt on 3 idiots movie last part Ppt on trans-siberian railway prices Ppt on united nations and its various organs Ppt on stars and planets Ppt on different occupations in the philippines