College Algebra
Study Guide Sections 4.1 – 4.4
Name
Period:______
Directions: Show all work and reasoning to receive full credit.
1) Determine the composite function ( f g )( x) given the functions f ( x)  4 x2  3x  5 and g ( x)  3 x  8 .
2) Determine
 f  g  2 given the functions
f ( x)   2 x  82 and g ( x)  3x 2  1 .
3) Determine if the given functions are inverses.
4
1
𝑓(𝑥) =
+ 2 𝑎𝑛𝑑 ℎ(𝑥) = −
−𝑥 − 2
𝑥+3
4) Use the given function to answer the following questions.
3x  2
g ( x) 
x5
a) Determine the inverse of the function.
b) Determine the domain and range of 𝑔(𝑥).
c) Determine the domain and range of 𝑔−1 (𝑥).
d) Verify algebraically that your inverse is correct.
1
5) The volume of a cone shaped balloon is given by 𝑉(𝑟) = 3 𝜋𝑟 2 ℎ. Find the volume of the balloon as a
3
1
function of time if the radius and height varies with time according to the function 𝑟(𝑡) = 4 𝑡 2 and ℎ(𝑡) = 2 𝑡 3 .
6) Solve the following equations algebraically.
a)
 ex    e9 
x
−3𝑥
c) 10
2
𝑥
 e9 x
1
∙ 10 = 10
b) 3−2𝑥+1 ∙ 3−2𝑥−3 = 3−𝑥
d)
𝑥
𝑥
9 ∙ 243 =
32𝑥−1
81
e) log
1
100
= 8𝑥 + 2
g) log 2 (𝑥 2 + 4𝑥 − 4) = 3
f) log 2
1
32
=
12
5
𝑥−2
7) Write as a sum and/or difference of logarithms. Express all powers as factors, factor completely, and
combine like terms.
 (3x  6) 4 x 2  1 

ln 
3
 x 2  x  2



8) Condense the logarithm by writing it as a single logarithm:


1
3log( x  1)  2 log( x  1)  3log 2 x .
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