Download presentation

Presentation is loading. Please wait.

1
**Form a Composite Functions and its Domain**

2
Composite Function Given two functions f and g, the composite function, denoted by f ◦ g (read as f composed with g) is defined by (f ◦ g)(x) = f(g(x)) The domain of f ◦ g is the set of all numbers x in the domain of g such that g(x) is in the domain of f.

3
**Evaluating a Composite Function**

Example 1 Suppose that f(x) = 2x3-3 and g(x) = 4x Find (f ◦ g)(1)= (g ◦ f)(1) = (f ◦ f)(-2) = (g ◦ g) (-1) =

4
**Finding a Composite Function**

Example 2 Suppose that f(x)= x2+3x-1 and g(x) = 2x+3 Find f ◦ g and state the domain of each composite function

5
**Finding a Composite Function**

Example 3 f(x)= x2+3x-1 and g(x) = 2x+3 g ◦ f and state the domain of each composite function

6
**Finding the Domain of f ◦ g**

Find the domain (f ◦g )(x) if f(x) = and g(x) =

7
Solution Domain of g is {x│x ≠ 1} Therefore 1 has to be excluded from the domain of the composite Domain of f is {x│x≠ -2} This means g(x) can never equal -2 we need to solve for g(x) = -2

8
**Finding a Composite Function**

Suppose that f(x)= and g(x) = Find f◦ g Find f ◦ f

9
**Showing that two Composite Functions are equal**

If f(x) = 3x-4 and g(x) = show that (f ◦ g)(x) = (g ◦ f)(x)= x

10
Homework Page 229 examples 7-45 every third question

11
**Inverse Functions Determine the Inverse of a Function**

Obtain the Graph of the Inverse Function from the graph of the Function Find the Inverse Function f-1

12
What is the Inverse? Something we know: We know that a function can be compared to a machine. We input an x and the machine manipulates it and outputs the value f(x) or the y value. The inverse of f receives as input a number f(x) and manipulates it and outputs the value x.

13
**Finding the inverse of a Function**

Let the domain of the function represent the people we know and let the range represent their birthdays. Domain Range Mrs Ireland December 7 Bry’Eisha March 11 Melissa October 7 Allena March 1

14
**Finding the inverse of a function**

Find the inverse of the following functions: {(-3,9), (-2,4), (-1,1), (0,0), (1,1), (2,4), (3,9)} The inverse of the given function is found by interchanging the entries in each ordered pair Answer: {(9,-3),(4,-2),(1,-1),(0,0),(1,1),(4,2)(9,3) Is the inverse a function? No because there are two outputs for 4, 9 and 1

15
**Finding the inverse of a function**

Example 2: Find the inverse of the function {(-3,-27),(-2,-8),(-1,-1),(0,0),(1,1),(2,8),(3,27) Answer: {(-27,-3),(-8,-2),(-1,-1),(0,0),(1,1),(8,2),(27,3) Is the inverse a function? Yes! Why?

16
One to one When the inverse of a function f is itself a function then f is said to be a one to one function. That is f is one to one if for any choice of elements x1 and x2 in the domain of f, with x1 ≠ x2, the corresponding values f(x1) and f(x2) are unequal, f(x1) ≠ f(x2) In words A function is one to one if any two different inputs never correspond to the same output

17
Horizontal Line Test Something we know: We know to test whether a graph is a function we use the vertical line test Now we have a new test Horizontal Line Test: If every horizontal line intersects the graph of a function f in at most one point, then f is one to one.

Similar presentations

Presentation is loading. Please wait....

OK

Copyright © 2014, 2010, 2007 Pearson Education, Inc.

Copyright © 2014, 2010, 2007 Pearson Education, Inc.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on db2 introduction to logic Ppt on business etiquettes of japan Ppt on computer languages popularity Ppt on principles of peace building grants Ppt on do's and don'ts of group discussion skills Ppt online downloader without java Ppt on relations and functions for class 11th sample Ppt on architectural heritage of india Ppt on central administrative tribunal delhi Mis ppt on nokia