1. 7.6 Function Operations

2. Review: What is a function?
A relationship where every domain (x value has exactly one unique range (y value).
Sometimes we talk about a FUNCTION MACHINE, where a rule is applied to each input of x

3. Function Operations

4. Adding and Subtracting Functions
When we look at functions we also want to look at their domains (valid x values). In this case, the domain is all real numbers.

5. Multiplying Functions
In this case, the domain is all real numbers because there are no values that will make the function invalid.

6. Dividing Functions
In this case, the domain is all real numbers EXCEPT -1, because x=-1 would give a zero in the denominator.

7. Composite Function – When you combine two or more functions
The composition of function g with function is written as 1
1. Evaluate the inner function f(x) first.
2. Then use your answer as the input of the outer function g(x). 2

8. Example – Composition of Functions
Method 1:
Method 2: