The Algebra of Functions

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Chapter 1

• Section 1.6
• The Algebra of Functions

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When to Restrict Domain?

• Fractions
• Cant have zero in the denominator!
• Even Roots
• Cant have a negative number under an even root
  radical!

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Operations on Functions
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A is the domain of f(x)B is the domain of g(x)
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Difference QuotientThe average rate of change
(the slope of the secant line)
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Difference Quotient
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Given two functions
f
and
g
, the
composite function
, denoted by
(read as
f
composed with
g
), is defined by
The domain of
is the set of
x
all numbers
in the domain of
g
(
g
such that
x
) is in the domain
of
f
.
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How to find the domain of a composite function

1. Find the domain of the function that is being
   substituted (Input Function) into the other
   function.
2. Find the domain of the resulting function (Output
   Function).
3. The domain of the composite function is the
   intersection of the domains found above.

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