Algebra Composite Functions and The Outer Function Question

12/5/21, 4:48 PMChapter 10 Quiz
Chapter 10 Quiz
Due Dec 2 by 11:59pm
Points 12
Available after Nov 30 at 12am
Submitting an external tool
Review Assessment Attempts
Flakoll, Jacob
Practice Quiz Chapter 10
Started: 12/2/21, 2:20 pm
Last Changed: 12/2/21, 3:20 pm
Total time questions were on-screen: 58.8 minutes
Due Date: Thu 12/2/21, 11:59 pm
Score in Gradebook: 11.5/12
Grade is calculated on the best assessment attempt (Attempt 1)
Attempt 1. Score: 11.5/12. Submitted 12/2/21, 3:20 pm
Show Intro and Between-Question Text
Question 1. Score: 1/1
If
f (x) = x
2
+ 8x
(a)
(f ∘ g)( − 1)
(b)
(g ∘ f )( − 1)
and
g(x) = x + 6
, evaluate each of the following.
= 65
= -1
Score: 0.5/0.5 0.5/0.5
Time spent on this version: 6.4 minutes.
Had help available: Video
Question 2. Score: 1/1
Given the following functions, use function composition to determine if
fucntions.
f (x) = x
3
+ 7
and
f (x)
and
g(x)
are inverse
3
g(x) = √x + 3
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12/5/21, 4:48 PM
Chapter 10 Quiz
+ 10
(a)
(f ∘ g)(x) =
x
(b)
(g ∘ f )(x) =
3
√
(c) Thus
3
x
+ 10
the inverse function of
is not
g(x)
f (x)
Score: 0.333/0.333 0.333/0.333 0.333/0.333
Time spent on this version: 2.8 minutes.
Had help available: Video
Question 3. Score: 1/1
Find the inverse of
y = x
3
− 4
3
√x+4
y =
Score: 1/1
Time spent on this version: 0.8 minutes.
Question 4. Score: 1/1
Use the like bases property to solve the equation
3(3)
n
− 20 = 709
5
n =
Score: 1/1
Time spent on this version: 1.4 minutes.
Had help available: Video
Question 5. Score: 1/1
Evaluate the following expressions without using a calculator. Your answers must be exact and in
simplest form.
(a)
ln e
(b)
e
(c)
e
3
ln 3
=
=
ln √3
=
3
3
√3
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12/5/21, 4:48 PM
(d)
Chapter 10 Quiz
1
ln(
e
5
) =
-5
Score: 0.25/0.25 0.25/0.25 0.25/0.25 0.25/0.25
Time spent on this version: 3.6 minutes. Show all tries
Had help available: Video Video
Question 6. Score: 1/1
Evalulate each of the following:
log3 (1) =
0
log3 (3) =
1
log3 (81) =
4
log3 (27) =
3
2
log3 (9) =
Score: 0.2/0.2 0.2/0.2 0.2/0.2 0.2/0.2 0.2/0.2
Time spent on this version: 1.5 minutes.
Question 7. Score: 1/1
Suppose
log a = 8
,
log b = 7
,
log c = 1
. Find
log(
a
5
3
b c
log(
a
5
2
)
.
3
b c
2
) =
-13
Show Detailed Solution
Score: 1/1
Time spent on this version: 9.3 minutes. Show all tries
Had help available: Video Written Example
Question 8. Score: 1/1
Suppose
log a =
log √ab =
− 8
and
log b = 5
. Find
log √ab
.
−1.5
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12/5/21, 4:48 PM
Chapter 10 Quiz
Show Detailed Solution
Score: 1/1
Time spent on this version: 0.7 minutes.
Had help available: Video Written Example
Question 9. Score: 1/1
Solve and Check:
log2 (x) + log2 (x + 2) = 3
If there is a solution, enter as an integer or reduced fraction. If there are multiple solutions, separate
them using commas. For no solutions, click No solution.
2
No solution
Score: 1/1
Time spent on this version: 0.9 minutes.
Had help available: Video Video
Question 10. Score: 0/0
ENTERING LOGARITHM FUNCTIONS.
When entering logarithms, use log( ) for common logarithms, ln( ) for natural logarithms, and use the
underscore character after the log to specify a specific base, such as log_2( ) for base 2, log_3( ) for
base 3, etc. You also need to use the proper function notation that includes the parentheses after the
log function, for example log(100) is correct, but log100 is not correct.
Examples with logarithms:
Type
To get
log(x)
log(x)
ln(x)
ln(x)
log_2(x)
log (x)
2
Unless the problem gives specific directions, any algebraically equivalent expression is acceptable. For
example, if the answer was log(5x), then log(5) + log(x) would also be acceptable.
Try it here. Enter the expression below and then press the Preview button to see how the computer is
interpreting what you typed.
Enter: log(x) + ln(x) + log_3(x)
log
( x ) + ln ( x ) + log3 ( x )
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12/5/21, 4:48 PM
Chapter 10 Quiz
Score: 0/0
Time spent on this version: 0.7 minutes.
Question 11. Score: 1/1
Find the solution of the exponential equation
11e
x
− 11 = 11
The exact solution, in terms of the natural logarithm is:
ln
x =
The approximate solution, rounded to 4 decimal places is:
x =
(2)
0.6931
Score: 0.5/0.5 0.5/0.5
Time spent on this version: 2.7 minutes.
Had help available: Video
Question 12. Score: 0.5/1
The fox population in a certain region has a continuous growth rate of 4 percent per year. It is estimated
that the population in the year 2000 was 27400.
(a) Find a function that models the population t years after 2000 (t
Hint: Use an exponential function with base e.
Your answer is
P (t) =
27400 ( 1.04 )
= 0
for 2000).
0
(b) Use the function from part (a) to estimate the fox population in the year 2008.
Your answer is (the answer must be an integer) 37733
Score: 0/0.5 0.5/0.5
Time spent on this version: 7.2 minutes.
Had help available: Video
Show all tries
Question 13. Score: 1/1
An unknown radioactive element decays into non-radioactive substances. In
of a sample decreases by 63 percent.
760
days the radioactivity
(a) What is the half-life of the element?
half-life: 530
(b) How long will it take for a sample of
time needed: 561.1
(days)
100
mg to decay to
48
mg?
(days)
Score: 0.5/0.5 0.5/0.5
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12/5/21, 4:48 PM
Chapter 10 Quiz
Time spent on this version: 20.8 minutes.
Had help available: Video
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