NAME __________________________
MATH 185
CHAPTER 4 REVIEW
MC FORM A
For the given functions f and g, find the requested composite function value.
1. f(x) =
A)
x + 4; g(x) = 3x;
13
Find (f ∘ g)(3).
B) 3 21
C) 3 7
D)
21
C) {x x ≥ 4, x ≠ 9}
D) {x x ≠ 9, x ≠ 4}
Find the domain of the composite function f ∘ g.
4
2. f(x) = x - 4; g(x) =
x-9
A) {x 9 < x ≤ 10}
B) all real numbers
Decide whether or not the functions are inverses of each other.
1
3. f(x) = 7x + 4; g(x) = (x - 4)
7
A) Yes
B) No
1
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.
4. f(x) = x3 + 2
y
10
5
-10
-5
5
10
x
-5
-10
A)
B)
y
-10
y
10
10
5
5
-5
5
10
x
-10
-5
5
-5
-5
-10
-10
5. Determine the equation for the inverse function of y = (x + 2)3 - 8.
3
3
3
B) y = x + 8 - 2
C) y = x - 2 + 8
A) y = x + 10
2
x
10
D) y =
3
x+6
Find the inverse function of f. State the domain and range of f.
3x - 2
6. f(x) =
x+5
x+5
2
A) f -1(x) =
; domain of f: {x x ≠ -5}; range of f: {y y ≠ }
3x - 2
3
3x + 2
B) f -1(x) =
; domain of f: {x x ≠ -5}; range of f: {y y ≠ 5}
x-5
5x + 2
C) f -1(x) =
; domain of f: {x x ≠ -5}; range of f: {y y ≠ 3}
3-x
5x + 2
D) f -1(x) =
; domain of f: {x x ≠ -5}; range of f: {y y ≠ - 3}
3+x
7. The graph of an exponential function is given. Which of the following is the correct equation of the
function?
5
y
5 x
-5
-5
A) y = 0.32x
C) y = 2.4x
B) y = 3.5x
3
D) y = 0.65x
Solve the equation.
1
8. 5x =
25
A) 2
B)
1
2
C) -2
D)
1
5
Change the exponential expression to an equivalent expression involving a logarithm.
2
9. 6 = 36
A) log
6
36 = 2
B) log
6
2 = 36
C) log
4
2
36 = 6
D) log
36
6=2
Find the exact value of the logarithmic expression.
1
10. log8
512
A) -64
B) 3
C) 64
D) -3
B) (6, ∞)
C) (-∞, -6)
D) (-∞, -6) or (6, ∞)
Find the domain of the function.
x+6
11. f(x) = log10
x-6
A) (-6, 6)
5
Solve the equation.
12. log
2
x=3
A) 9
B) 6
C) 5
D) 8
Solve the Application.
13. The Richter scale converts seismographic readings into numbers for measuring the magnitude of an
earthquake according to this function
x
M(x) = log ( ), where xo = 10-3.
xo
What would be the readings x (to the nearest tenth) for magnitudes of 4.6 and 7.6?
A) 39.8 and 39810.7
B) 662.8 and 880.8
6
C) 55.9 and 55907.2
D) 2.7 and 2.9
Use the properties of logarithms to find the exact value of the expression. Do not use a calculator.
14. log11 33 - log11 3
A) 1
B) 3
C) 11
D) 33
Write the expression as a single logarithm.
15. 9 log 2 + 2 log 8
a
a
9
2
A) log 2 · log 8
a
a
9 2
B) log (2 · 8 )
a
C) log (18 + 16)
a
D) log
7
29
a 82
Use the Change-of-Base Formula and a calculator to evaluate the logarithm. Round your answer to three
decimal places.
16. log3 25
A) 0.341
B) 3.221
C) 6.746
B) 7
C)
D) 2.930
Solve the equation.
17. log (3 + x) - log (x - 2) = log 2
A) -7
8
1
2
D) no solution
Solve the equation. If necessary, round your answer to two decimal places.
1 x
18. ( ) = 10
3
A) -3.33
B) -2.10
C) -0.48
D) 2.10
Solve the equation.
19. How long will it take for an investment to double in value if it earns 6.5% compounded continuously?
Round answer to three decimal places.
A) 10.664 years
B) 16.902 years
C) 5.332 years
9
D) 11.253 years
Solve the problem.
20. A fossilized leaf contains 24% of its normal amount of carbon 14. How old is the fossil (to the nearest
year)? Use 5600 years as the half-life of carbon 14.
A) 11,509 years
B) 34,925 years
C) 2213 years
10
D) 25,629 years
Answer Key
Testname: 185 CH 4 REV MCA
1. A
2. A
3. A
4. B
5. B
6. C
7. B
8. C
9. A
10. D
11. D
12. D
13. A
14. A
15. B
16. D
17. B
18. B
19. A
20. A
11