functions 2 inverse , composite

1Ago 28­06:11 p.m.

Composition of functionsInverse function

By the end of the lesson you will be able to:

• Understand and use composite functions.

• Understand and use  inverse  functions.

http://www.youtube.com/watch?v=GW3Sq6Ez9zA

2Ago 28­06:11 p.m.

Starter:

With your calculator draw the graph of  y= ex.State domain, range and asymptotes of this function.

3Ago 28­06:11 p.m.

Composition of functions

If   and

find in simplest form:

4Ago 28­06:11 p.m.

Given the functions andfind

5Ago 28­06:11 p.m.

x f(x)

f gg(f(x))

For  to exist, then  range of f must be  included in the domain of g.

6Ago 28­06:11 p.m.

Indentity function:

What happens when this function is composed with another function?

g(x) = 2 x ­ 3

=

=

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Inverse function

x f(x)

f

f ­1

The inverse of a function exists if and only if the function is a one-to-one function.

8Ago 28­06:11 p.m.

Which of these functions have an inverse?

9Ago 28­06:11 p.m.

Find the inverse of : draw the graphs of both functions. Draw the identity function on the same graph.

and

10Abr 30­05:32 p.m.

y = 3x+2y = x

11Ago 28­06:11 p.m.

The graph of is a reflection of the graph of

about the line y = x

Find the inverse function of

and sketch both graphs.

12Sep 12­02:30 p.m.

13Ago 28­06:11 p.m.

Find the inverse function of 

Draw the graphs of both functions.

is a self­inverse function

14Ago 28­06:11 p.m.

Find the inverse function of

for x≠1 and sketch both graphs.