1. The document discusses composition of functions and inverse functions. It provides examples of composing functions, finding inverse functions, and sketching the graphs of functions and their inverses. 2. Key concepts covered include the domain and range requirements for functions to be composable, identifying which functions have inverses, finding inverse functions both algebraically and graphically, and properties of inverse functions like being reflections over the line y=x. 3. Examples involve composing functions like f(g(x)), finding the inverses of functions like y=3x+2, and sketching the graphs of functions and their inverses.

1. 1
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Composition of functions
Inverse 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

2. 2
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Starter:
With your calculator draw the graph of y= ex
.
State domain, range and asymptotes of this function.

3. 3
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Composition of functions
If and
find in simplest form:

4. 4
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Given the functions and
find

5. 5
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x
f(x)
f g
g(f(x))
For to exist, then range of f must be
included in the domain of g.

6. 6
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Indentity function:
What happens when this function is composed with another
function?
g(x) = 2 x ­ 3
=
=

7. 7
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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.

8. 8
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Which of these functions have an inverse?

9. 9
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Find the inverse of :
draw the graphs of both functions. Draw the
identity function on the same graph.
and

10. 10
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y = 3x+2
y = x

11. 11
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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.

12. 12
Sep 12­02:30 p.m.

13. 13
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Find the inverse function of
Draw the graphs of both functions.
is a self­inverse function

14. 14
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Find the inverse function of
for x≠1 and sketch both graphs.