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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

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Starter:

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

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Composition of functions

If   and

find in simplest form:

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Given the functions andfind

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x f(x)

f gg(f(x))

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

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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.

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Which of these functions have an inverse?

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

and

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y = 3x+2y = x

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The graph of is a reflection of the graph of

about the line y = x

Find the inverse function of

and sketch both graphs.

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Find the inverse function of 

Draw the graphs of both functions.

is a self­inverse function

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Find the inverse function of

for x≠1 and sketch both graphs.