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Math Problems
Algebra 2
Evaluate functions
Given the substitutions
ln
2
=
a
,
ln
3
=
b
\ln 2=a, \ln 3=b
ln
2
=
a
,
ln
3
=
b
, and
ln
5
=
c
\ln 5=c
ln
5
=
c
, find the value of
ln
(
81
e
3
)
\ln (81 \sqrt[3]{e})
ln
(
81
3
e
)
in terms of
a
,
b
a, b
a
,
b
, and
c
c
c
.
\newline
Answer:
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- Let
f
f
f
be a function such that
f
(
−
1
)
=
3
f(-1)=3
f
(
−
1
)
=
3
and
f
′
(
−
1
)
=
5
f^{\prime}(-1)=5
f
′
(
−
1
)
=
5
.
\newline
- Let
g
g
g
be the function
g
(
x
)
=
2
x
3
g(x)=2 x^{3}
g
(
x
)
=
2
x
3
.
\newline
Let
F
F
F
be a function defined as
F
(
x
)
=
f
(
x
)
g
(
x
)
F(x)=\frac{f(x)}{g(x)}
F
(
x
)
=
g
(
x
)
f
(
x
)
.
\newline
F
′
(
−
1
)
=
F^{\prime}(-1)=
F
′
(
−
1
)
=
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y
=
4
x
+
1
y=\sqrt{4 x+1}
y
=
4
x
+
1
\newline
d
y
d
x
=
?
\frac{d y}{d x}=?
d
x
d
y
=
?
\newline
Choose
1
1
1
answer:
\newline
(A)
2
4
x
+
1
2 \sqrt{4 x+1}
2
4
x
+
1
\newline
(B)
2
x
\frac{2}{\sqrt{x}}
x
2
\newline
(c)
2
4
x
+
1
\frac{2}{\sqrt{4 x+1}}
4
x
+
1
2
\newline
(D)
1
2
4
x
+
1
\frac{1}{2 \sqrt{4 x+1}}
2
4
x
+
1
1
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Which value of
k
k
k
makes
5
−
k
+
12
=
16
5-k+12=16
5
−
k
+
12
=
16
a true statement?
\newline
Choose
1
1
1
answer:
\newline
(A)
k
=
1
k=1
k
=
1
\newline
(B)
k
=
2
k=2
k
=
2
\newline
(C)
k
=
3
k=3
k
=
3
\newline
(D)
k
=
4
k=4
k
=
4
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Which value of
j
j
j
makes
(
5
+
3
)
j
=
48
(5+3) j=48
(
5
+
3
)
j
=
48
a true statement?
\newline
Choose
1
1
1
answer:
\newline
(A)
j
=
3
j=3
j
=
3
\newline
(B)
j
=
4
j=4
j
=
4
\newline
(C)
j
=
5
j=5
j
=
5
\newline
(D)
j
=
6
j=6
j
=
6
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What is the sum of the solutions to the equation
\newline
(
t
+
3
)
(
t
−
357
)
=
0
?
(t+3)(t-357)=0 \text { ? }
(
t
+
3
)
(
t
−
357
)
=
0
?
\newline
Choose
1
1
1
answer:
\newline
(A)
−
360
-360
−
360
\newline
(B)
−
354
-354
−
354
\newline
(C)
354
354
354
\newline
(D)
360
360
360
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2
3
−
5
x
=
b
x
+
1
3
\frac{2}{3}-5x=bx+\frac{1}{3}
3
2
−
5
x
=
b
x
+
3
1
\newline
In the equation shown,
\newline
b
b
b
is a constant. For what value of
\newline
b
b
b
does the equation have no solutions?
\newline
Choose
1
1
1
answer:
\newline
(A)
5
5
5
\newline
(B)
0
0
0
\newline
(C)
−
5
-5
−
5
\newline
(D)
2
3
\frac{2}{3}
3
2
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Use the following function rule to find
f
(
11
)
f(11)
f
(
11
)
.
\newline
f
(
x
)
=
−
10
−
7
x
f(x) = -10 - 7x
f
(
x
)
=
−
10
−
7
x
\newline
f
(
11
)
=
f(11) =
f
(
11
)
=
_____
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