(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
Check Your
Understanding: (Remember to write down your answers to these
questions.)
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 
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