1. Fun with Functions!

2. What are we going to learn today?
~How to perform operations with functions.
~ How do we find the composition of functions?
~ What is the domain of a function?

3. Addition and Subtraction
Suppose we have...
and
Now, let...
What is f(x)+g(x) and f(x)-g(x)?

4. Example 1)
Let
and
Find:
Example 2)
Let
and
Find:

5. Multiplication and Division
If and , how do you think we will find ?
How about ?

6. Example 3)
Let
and
Find:

7. the set of input values of a function.
Hold Your Horses!
Look at
Using your graphing calculator, look at the table of values and describe what you see that happens.
Domain:
the set of input values of a function.
So what is the domain here?

8. But thinking may be required!
How to find the domain?
What are some of the situations that may change the domain?
Here are some examples...
1) No restrictions on the input
2) Denominator cannot be zero
3) No negative numbers under a radical
But thinking may be required!

9. Example 5)
Find the domain of the following: a) b) c)

10. Composition of Functions
A fifth operation that can be performed on functions.
Defined as:
The composition of the function f with the function g is:
h(x)=f(g(x))
In other words, the inside function is substituted for x in the outer function.
Example)
Let

11. What about domain?
Let
and
Find f(g(x)):
And the domain...

12. Try these! 1) Let and 2) Let and (And find the domain) g(f(x))=
f(g(x))=
g(g(x))= 2)
Let and
g(f(x))=
f(g(x))=