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 Depdendent Variable

 Number of equations to solve: 23456789
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 Solve for:

 Dependent Variable

 Number of inequalities to solve: 23456789
 Ineq. #1:
 Ineq. #2:

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 Solve for:

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# Composite Functions

Given two functions f and g,
the composite function is defined
by the equation The domain of is the set of all x
in the domain of such that g(x) is
in the domain of f. Given f(x)=3x + 1 and g(x)= -2x-5
Find a formula for( )(x)
find ( )(2) and ( )(-1)
Find a formula for ( )(x)
Find ( )(2) and ( )(-1)
Does ( )(x)=( )(x)? Example
Given and g(x)=x2
Find a formula and the domain for
( )(x).  To find the domain of ( )(x),
we must find the set of all x in the
domain of g such that g(x) is in the
domain of f. The domain of g(x)=x2 is the set of all
reals. The domain of is For what values of x is g(x)
in the domain of f?

We need to find the values of x such that The solution set in this case is Check the graph of  Given and g(x)=x2
Find a formula and the domain for
( )(x).

In this case, you can't just look at the
formula for ( )(x) to determine
it's domain. Example
Given and Find a formula for ( )(x)
Find( )(2) and ( )(-1)
Find the domain of ( )(x) Example
Given and g(x)=|x|
Find a formula for ( )(x) and
( )(x), find the domains and
sketch their graphs