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Math 131 WIR, copyright Angie Allen
Math 131 Week-in-Review #2 (Sections 1.3, 1.5, and 1.6)
1. Determine whether the following functions are one-to-one.
a) T (x) is the average temperature on the xth day of September.
b) f (x) =
c)
1
x
Day
# of Push-ups
Mon.
20
2. Find the domain of g(x) =
Tues.
15
Wed.
25
Thurs.
10
Fri.
12
√
5
x−7
.
log2 (4x − 1)
3. If Jake Ryan, the owner of a bakery, has x birthday cake orders for the week, he will keep f (x) = 3x + 5 packages of
birthday candles (in packages of 16) in stock for customers to purchase. If he keeps x packages of birthday candles in
stock, he keeps g(x) = 2x + 4 birthday balloons in stock. Find an expression for the number of balloons Jake will stock
as a function of the number of birthday cake orders.
Math 131 WIR, copyright Angie Allen
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4. Ibuprofen has a half-life of 1.8 hours. Amy took one 800 mg dose of ibuprofen this morning at 8:00 AM for heel pain.
a) Find a function representing the amount of ibuprofen, I(h), that remains in her system h hours after taking the
dose.
b) Determine how much ibuprofen will be in her system at 2:30 PM today.
c) Find a function that represents the number of hours after Amy took the 800 mg dose based on the amount of
ibuprofen remaining in her system.
Math 131 WIR, copyright Angie Allen
5. Given h(x) = loga (3 + logb x), where a, b > 0 and a, b 6= 1,
a) express the function h in the form f ◦ g, and find the domain of h.
b) find h−1 and its domain.
6. Find the domain of the following function:

x+2


x ≤ −1

 ex
f (x) =


x+4


x>1
x2 − 9
3
4
Math 131 WIR, copyright Angie Allen
7. If logb 4 = 1.2619 and logb 6 = 1.6310, find logb
8. If f (x) = x2 + 3x and g(x) =
9. If g(x) =
16
.
6b2
x+3
f
, find and its domain.
x−5
g
√
x+2
and h(x) = x + 4, find g ◦ h and its domain.
ln |x|
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Math 131 WIR, copyright Angie Allen
10. Indicate verbally how the graph of g(x) = − 31 ex+4 + 8 is related to the graph of f (x) = ex .
11. If the point (a, b) is on the graph of a function f ,
a) what point must be on the graph of the function g if g(x) = f (−x)?
b) what point must be on the graph of the function k if k(x) = − f (x) + 3?
12. Use the table below to evaluate each expression.
x
f (x)
g(x)
−12 −8
0
2
4
6
7
8
10
−42 −30 −6 0
6
12
15
18
24
20
12 −4 −8 −12 −16 −18 −20 −24
a) (g ◦ f )(2)
b) ( f ◦ f )(4)
c) f −1 (18)
d) f ( f −1 (−36))
e) g−1 (−g(−8))
Math 131 WIR, copyright Angie Allen
13. Solve the following equations for x:
2
a)
3x
1
= −4x .
27 3
b) 2x + 4x = 272. (Hint: 16 × 17 = 272.)
c) log3 (x + 5) + log3 (x − 5) = log10 100.
6
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Math 131 WIR, copyright Angie Allen
14. Find the domain of the following functions.
8 log3 (x − 5)
a) f (x) =
x2
e x−π
x
e x−3
b) f (x) = √
3
5−x
√
e x+9
c) f (x) = √
5
x+1
√
4
x+7
d) f (x) = x−3
2
8
Math 131 WIR, copyright Angie Allen
15. Simplify the following using properties of logarithms:
1
3 log7 x − 2 log7 y + log7 z + 4 log7 75
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16. Simplify the following expression leaving no negative exponents:
3x2 y−3
x−4 z3
−2
17. Starting with the function f (x) = |x|, write the function, g(x), that results from shifting f (x) to the left 2 units, reflecting
about the y-axis, and compressing horizontally by a factor of 4.
Math 131 WIR, copyright Angie Allen
18. Solve the following for x:
a) 8 1.045x+1 = 24
b) 23 loga 25 − 2 loga 5 = loga x, where a > 0 and a 6= 1.
c) log8 (x + 3) = log8 5 + log8 (x − 1)
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