## (Section 11)

Functions are a fundamental concept in all mathematics courses, including calculus. You need to understand of how to describe the domain, describe the range, describe the rule, and form composite functions.

A FUNCTION is a rule, usually written algebraically like y=3x-2, that assigns each number in a DOMAIN to exactly one number in the RANGE.

For example, , the domain of this function is all real numbers, and the range is all non-negative real numbers (zero and all positive real numbers). The rule is to first square the number in the domain and then take the principal square root (positive answer only) of the answer.

## Composite Functions

A composite function is denoted .

Meaning: A number x is placed in the function f first and then that result is placed in the function g. The final results is g(f(x)).

In problems involving composite functions, it is important to handle the domain and range carefully. When numbers are placed in the f function, the results, f(x), must be in the domain of the g function. If the domain and range are not handled carefully you may work with an incorrect graph.

## Examples of Composite

Describe the domain and range of f and g. Then form the function f(g(x)) and describe the domain and range of this composed function, if

1.  and

2.  and

3. and