1. 4-4 Functions
Fogs, gofs and inverses

2. What is a function?
A set of (x,y) pairs where each x has a unique y value.
Functions can be added, subtracted, multiplied and divided.

3. Examples 1. If and find a) f(x) + g(x) c) f(x) ÷ g(x) b) f(x) · g(x)
2. For the above functions find
a) f(3) · g(3)
b) Plug 3 into 1b (above)
Note: When you add, subtract, multiply and divide functions, the domain of the result is the domain common to the functions that you used.

4. Fog? Gof? What is that? “fog” is the nickname for f◦g and
“gof” is the nickname for g◦f.
That notation indicates “composition”. That is, we are taking the composition of 2 (or more) functions. You have seen composition before but it isn’t something that jumps out at you.

5. This is a composition
can be thought of as the composition of the functions
and
You sort of “tuck” one function into the other.

6. If and
Then
Now, what would g◦f be?

7. Examples 4. If and find a) f(x) ◦ g(x) b) g(x) ◦ f(x) If , and
find f ◦ g ◦ h.
6. If and find f ◦ g

8. Domain of a composite
The domain of a composite is all x in the domain of the inner function for which the values are in the domain of the outer function.
Just determine domain of inner function, then exclude anything that is not in the domain of the outer function.
Note: Please add #59 to the homework assignment