# Combining Functions

```Combining Functions
Section 1.7
Objectives
• Determine the domain and range (where possible) of a
function given as an equation.
• Add, subtract, multiply, and/or divide function.
• State the domain two function combined in an
arithmetic method.
• Put together two (or more) functions using
composition.
• Determine the value of the composition of two (or
more) functions given the graphs of the functions.
• Determine the value of the composition of two (or
more) function given the equations of the functions.
• State the domain two function combined through
composition.
Objectives
• Decompose the composition of two functions into it
constituent functions.
• Solve a word problem involving the composition of
functions.
Vocabulary
• domain
• range
• function composition
Domain Questions
1. Does the function have a denominator?
2. Does the function have a square or
even root?
3. Does the function have a log or ln in
it?
4. Did the function arise from finding an
inverse?
5. Is this a “real world” problem?
Find the domain of the function:
x  11
h (x )  2
x  196
Find the domain of the function:
f (x )  67.5  5x
Find the domain of the function:
g (x )  8x 2  4
Find the domain of the function:
k (x )  4 x  17
15
f (x ) 
x 5
Given the functions
8
and g (x )  x  9 find each of the
following:
(f  g )(x )
(f  g )(x )
(fg )(x )
f 
 (x )
g
 
15
f (x ) 
x 5
Given the functions
8
and g (x )  x  9 find the domain of
each of the following:
(f  g )(x )
(f  g )(x )
(fg )(x )
f 
 (x )
g
 
For the functions f(x) and g(x)
are given in the graph
below. Find the indicated
corresponding function values
(f  g )(1)
(f  g )(3)
Given the functions f (x )  6x  9
2
and g (x )  3  x find each of each
of the following:
(f  g )(2)
( g  f )(2)
1
f (x ) 
x
Given the functions
and g (x )  7x  6 find each of the
following:
(f  g )(x )
( g  f )(x )
(f  f )(x )
1
f (x ) 
x
Given the functions
and g (x )  7x  6 find the domain
of each of the following:
(f  g )(x )
( g  f )(x )
(f  f )(x )
For the functions f(x) and g(x)
are given in the graph
below. Find the indicated
corresponding function values
f ( g ( 3))
g (f (2))
Express the function h (x )  (x  5)
2
in the form f  g . If f (x )  x ,
find g(x).
2
A spherical weather balloon is