Ch 5 Exam Review
The graph of a one-to-one function f is given. Draw the
graph of the inverse function f-1 as a dashed line or curve.
Evaluate the expression using the values given in the
table.
1) (f g)(3)
8) f(x) =
x+3
x
1 5 11 12
f(x) -1 11 3 14
x
-5 -1 1 3
g(x) 1 -7 5 11
For the given functions f and g, find the requested
composite function value.
Find (f g)(2).
2) f(x) = x + 3, g(x) = 3x;
3) f(x) = 2x + 4, g(x) = 4x2 + 3;
1).
Find (g
Find the domain of the composite function f
x
2
; g(x) =
4) f(x) =
x+1
x+3
5) f(x) =
x - 3; g(x) =
g)(
Use the graph of the given one-to-one function to sketch
the graph of the inverse function. For convenience, the
graph of y = x is also given.
9)
g.
3
x-9
Indicate whether the function is one-to-one.
6) {(-1, -9), (0, -9), (1, 9), (2, -3)}
Use the horizontal line test to determine whether the
function is one-to-one.
7)
Decide whether or not the functions are inverses of each
other.
1
10) f(x) = 3x + 9, g(x) = x - 3
3
The function f is one-to-one. Find its inverse.
11) f(x) = 2x - 4
12) f(x) =
1
9x - 8
3x - 8
Graph the function.
3 x
16) f(x) =
5
Determine i) the domain of the function, ii) the range of
the function, iii) the domain of the inverse, and iv) the
range of the inverse.
5
13) f(x) =
x-2
The graph of an exponential function is given. Match the
graph to one of the following functions.
14)
Solve the equation.
17) 3 1 + 2x = 27
x
18) (ex) · e24 = e11x
A) f(x) = 3 x
C) f(x) = 3 x + 2
B) f(x) = 3 x - 2
D) f(x) = 3 x + 2
1 x+3
19) ex - 5 =
e4
Use transformations to graph the function. Determine the
domain, range, and horizontal asymptote of the function.
15) f(x) = 5 -x + 3
Graph the function.
20) f(x) = -1 + ex
Change the exponential expression to an equivalent
expression involving a logarithm.
1
21) 3 -3 =
27
22) ex = 10
2
Change the logarithmic expression to an equivalent
expression involving an exponent.
23) log 2 x = 3
Use the properties of logarithms to find the exact value of
the expression. Do not use a calculator.
34) ln e2 2
24) log 1/4 16 = -2
25) ln
35) log4 24 - log4 6
36) 10log 12 - log 2
1
= -4
e4
Suppose that ln 2 = a and ln 5 = b. Use properties of
logarithms to write each logarithm in terms of a and b.
5
37) ln
2
Find the exact value of the logarithmic expression.
26) log1/4 256
27) log 10 10,000
38) ln
28) ln e7
20
Write as the sum and/or difference of logarithms. Express
powers as factors.
14 x
39) log 5
y
Find the domain of the function.
29) f(x) = ln(-3 - x)
30) f(x) = log10
7
x+5
x-7
40) log 4
The graph of a logarithmic function is shown. Select the
function which matches the graph.
31)
x+6
x3
3
41) log 5
r
4
u2
s
Express as a single logarithm.
3
1
42) 6 log a m - log a n + log a j - 5 log a k
5
4
43) 6 log b q - log b r
44) ln
A) y = -log x
C) y = log(-x)
4), x > 0
B) y = -log(-x)
D) y = log x
Use the Change-of-Base Formula and a calculator to
evaluate the logarithm. Round your answer to three
decimal places.
45) log 0.771
6
Solve the equation.
32) log5 (x2 - 4x) = 1
33) ln
x2 + 5x - 14
x2 + 6x - 7
- ln
+ ln (x2 - 4x +
x-1
x+1
x+2=2
Solve the equation.
46) log 6 (x + 3) = 3
3
47) log 5 (2x + 4) = log 5 (2x + 7)
48) log (3x) = log 4 + log (x - 3)
49) 2 + log3 (2x + 5) - log3 x = 4
50) log 5 (x + 1) = 1 + log 5 (x - 1)
1
51) 2 (5 - 3x) =
16
Solve the equation. Express irrational answers in exact
form and as a decimal rounded to 3 decimal places.
3 x
= 41 - x
52)
2
4
Answer Key
Testname: CH 5 EXAM REVIEW
1)
2)
3)
4)
5)
6)
7)
8)
3
3
199
{x x -3, x -5}
{x 9 < x 10}
No
No
9)
10) Yes
x+4
11) f-1 (x) =
2
8x - 8
12) f-1 (x) =
3x - 9
13) f(x): D = {x|x 2}, R = {y 0};
f-1 (x): D = {x|x 0}, R = {y|y 2}
14) D
5
Answer Key
Testname: CH 5 EXAM REVIEW
15) domain of f: (- , ); range of f:(3, )
horizontal asymptote: y = 3
16)
17) {1}
18) {3, 8}
7
19) 5
20)
1
= -3
21) log 3
27
22) ln 10 = x
23) 2 3 = x
6
Answer Key
Testname: CH 5 EXAM REVIEW
24)
1 -2
= 16
4
1
25) e-4 =
e4
26)
27)
28)
29)
30)
31)
32)
-4
4
7
( , -3)
(- , -5) (7, )
B
{5, -1}
33) {e4 - 2}
34) 2 2
35) 1
36) 6
37) b - a
1
38) (2a + b)
7
1
39) log 5 14 + log 5 x - log 5 y
2
40) log 4 (x + 6) - 3 log 4 x
1
1
41) log 5 r + log 5 s - 2 log 5 u
3
4
m 6 j1/4
42) log a
n 3/5 k5
q6
43) log b
r
44) ln
(x - 2)3 (x + 1)
(x - 1)2
45) -0.145
46) {213}
47)
48) 12
5
49)
7
50)
3
2
51) {3}
52)
ln 4
3
ln
+ ln 4
2
0.774
7