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Math Problems
Algebra 2
Find the vertex of the transformed function
Given
x
>
0
x>0
x
>
0
, the expression
x
4
3
\sqrt[3]{x^{4}}
3
x
4
is equivalent to
\newline
x
2
x
2
3
x^{2} \sqrt[3]{x^{2}}
x
2
3
x
2
\newline
x
x
x
\newline
x
x
3
x \sqrt[3]{x}
x
3
x
\newline
x
2
x^{2}
x
2
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Given
x
>
0
x>0
x
>
0
, the expression
x
13
5
\sqrt[5]{x^{13}}
5
x
13
is equivalent to
\newline
x
2
x
3
5
x^{2} \sqrt[5]{x^{3}}
x
2
5
x
3
\newline
x
3
x^{3}
x
3
\newline
x
x
4
5
x \sqrt[5]{x^{4}}
x
5
x
4
\newline
x
2
x^{2}
x
2
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Evaluate the left hand side to find the value of
a
a
a
in the equation in simplest form.
\newline
x
x
1
4
=
x
a
\frac{x}{x^{\frac{1}{4}}}=x^{a}
x
4
1
x
=
x
a
\newline
Answer:
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Evaluate the left hand side to find the value of
a
a
a
in the equation in simplest form.
\newline
(
x
2
)
1
6
=
x
a
\left(x^{2}\right)^{\frac{1}{6}}=x^{a}
(
x
2
)
6
1
=
x
a
\newline
Answer:
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16
16
16
. Find the equation of the curve for which
y
′
′
=
4
x
3
y^{\prime \prime}=\frac{4}{x^{3}}
y
′′
=
x
3
4
and which is tangent to the line
2
x
+
y
=
5
2 x+y=5
2
x
+
y
=
5
at the point
(
1
,
3
)
(1,3)
(
1
,
3
)
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Determine the value of
y
y
y
, if
x
x
x
is
−
5
-5
−
5
.
\newline
y
=
x
2
−
1
y=x^{2}-1
y
=
x
2
−
1
\newline
Answer:
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Determine the value of
y
y
y
, if
x
x
x
is
7
7
7
.
\newline
y
=
x
2
+
2
y=x^{2}+2
y
=
x
2
+
2
\newline
Answer:
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Determine the value of
y
y
y
, if
x
x
x
is
11
11
11
.
\newline
y
=
x
2
−
11
y=x^{2}-11
y
=
x
2
−
11
\newline
Answer:
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Determine the value of
y
y
y
, if
x
x
x
is
5
5
5
.
\newline
y
=
x
2
−
9
y=x^{2}-9
y
=
x
2
−
9
\newline
Answer:
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Determine the value of
y
y
y
, if
x
x
x
is
2
2
2
.
\newline
y
=
x
2
−
9
y=x^{2}-9
y
=
x
2
−
9
\newline
Answer:
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Determine the value of
y
y
y
, if
x
x
x
is
2
2
2
.
\newline
y
=
(
x
+
10
)
2
y=(x+10)^{2}
y
=
(
x
+
10
)
2
\newline
Answer:
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Determine the value of
y
y
y
, if
x
x
x
is
4
4
4
.
\newline
y
=
x
2
−
1
y=x^{2}-1
y
=
x
2
−
1
\newline
Answer:
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Determine the value of
y
y
y
, if
x
x
x
is
3
3
3
.
\newline
y
=
x
2
+
11
y=x^{2}+11
y
=
x
2
+
11
\newline
Answer:
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Determine the value of
y
y
y
, if
x
x
x
is
−
1
-1
−
1
.
\newline
y
=
(
x
−
2
)
2
y=(x-2)^{2}
y
=
(
x
−
2
)
2
\newline
Answer:
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Determine the value of
y
y
y
, if
x
x
x
is
6
6
6
.
\newline
y
=
x
2
+
6
y=x^{2}+6
y
=
x
2
+
6
\newline
Answer:
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Determine the value of
y
y
y
, if
x
x
x
is
4
4
4
.
\newline
y
=
x
2
−
10
y=x^{2}-10
y
=
x
2
−
10
\newline
Answer:
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Determine the value of
y
y
y
, if
x
x
x
is
−
2
-2
−
2
.
\newline
y
=
x
2
−
9
y=x^{2}-9
y
=
x
2
−
9
\newline
Answer:
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Determine the value of
y
y
y
, if
x
x
x
is
4
4
4
.
\newline
y
=
x
2
−
3
y=x^{2}-3
y
=
x
2
−
3
\newline
Answer:
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Determine the value of
y
y
y
, if
x
x
x
is
6
6
6
.
\newline
y
=
x
2
−
3
y=x^{2}-3
y
=
x
2
−
3
\newline
Answer:
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Determine the value of
y
y
y
, if
x
x
x
is
1
1
1
.
\newline
y
=
x
2
−
2
y=x^{2}-2
y
=
x
2
−
2
\newline
Answer:
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Determine the value of
y
y
y
, if
x
x
x
is
9
9
9
.
\newline
y
=
x
2
−
8
y=x^{2}-8
y
=
x
2
−
8
\newline
Answer:
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Determine the value of
y
y
y
, if
x
x
x
is
4
4
4
.
\newline
y
=
x
2
−
11
y=x^{2}-11
y
=
x
2
−
11
\newline
Answer:
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Determine the value of
y
y
y
, if
x
x
x
is
6
6
6
.
\newline
y
=
x
2
+
10
y=x^{2}+10
y
=
x
2
+
10
\newline
Answer:
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Determine the value of
y
y
y
, if
x
x
x
is
−
11
-11
−
11
.
\newline
y
=
x
2
−
4
y=x^{2}-4
y
=
x
2
−
4
\newline
Answer:
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Determine the value of
y
y
y
, if
x
x
x
is
−
4
-4
−
4
.
\newline
y
=
x
2
+
4
y=x^{2}+4
y
=
x
2
+
4
\newline
Answer:
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Determine the value of
y
y
y
, if
x
x
x
is
8
8
8
.
\newline
y
=
x
2
+
6
y=x^{2}+6
y
=
x
2
+
6
\newline
Answer:
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Determine the value of
y
y
y
, if
x
x
x
is
−
4
-4
−
4
.
\newline
y
=
x
2
−
3
y=x^{2}-3
y
=
x
2
−
3
\newline
Answer:
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Determine the value of
y
y
y
, if
x
x
x
is
−
4
-4
−
4
.
\newline
y
=
x
2
+
6
y=x^{2}+6
y
=
x
2
+
6
\newline
Answer:
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Determine the value of
y
y
y
, if
x
x
x
is
9
9
9
.
\newline
y
=
x
2
−
7
y=x^{2}-7
y
=
x
2
−
7
\newline
Answer:
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Determine the value of
y
y
y
, if
x
x
x
is
11
11
11
.
\newline
y
=
x
2
−
7
y=x^{2}-7
y
=
x
2
−
7
\newline
Answer:
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Determine the value of
y
y
y
, if
x
x
x
is
10
10
10
.
\newline
y
=
x
2
+
7
y=x^{2}+7
y
=
x
2
+
7
\newline
Answer:
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Determine the value of
y
y
y
, if
x
x
x
is
−
9
-9
−
9
.
\newline
y
=
x
2
−
1
y=x^{2}-1
y
=
x
2
−
1
\newline
Answer:
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Determine the value of
y
y
y
, if
x
x
x
is
10
10
10
.
\newline
y
=
x
2
−
11
y=x^{2}-11
y
=
x
2
−
11
\newline
Answer:
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g
(
x
)
=
(
x
+
12
)
(
x
−
4
)
g(x)=(x+12)(x-4)
g
(
x
)
=
(
x
+
12
)
(
x
−
4
)
\newline
The function
g
g
g
is defined by the given equation. What is the minimum value of
g
(
x
)
?
g(x) ?
g
(
x
)?
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Decompose the function
f
(
g
(
x
)
)
=
(
1
x
)
6
f(g(x))=\left(\frac{1}{x}\right)^{6}
f
(
g
(
x
))
=
(
x
1
)
6
into
f
(
x
)
f(x)
f
(
x
)
and
g
(
x
)
g(x)
g
(
x
)
.
\newline
g
(
x
)
=
g(x)=
g
(
x
)
=
\newline
f
(
x
)
=
f(x)=
f
(
x
)
=
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Given the function
\newline
y
=
6
+
x
4
5
x
−
2
y=\frac{6+x^{4}}{5x-2}
y
=
5
x
−
2
6
+
x
4
, find
\newline
d
y
d
x
\frac{dy}{dx}
d
x
d
y
in simplified form.
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Given the function
\newline
f
(
x
)
=
4
(
−
x
2
−
9
x
+
3
)
5
,
f(x)=4(-x^{2}-9x+3)^{5},
f
(
x
)
=
4
(
−
x
2
−
9
x
+
3
)
5
,
find
\newline
f
′
(
x
)
f^{\prime}(x)
f
′
(
x
)
in any form.
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Find
d
y
d
x
\frac{dy}{dx}
d
x
d
y
for the given function.
\newline
d
y
=
□
=
x
2
−
csc
(
x
)
+
5
dy_=\square=x^{2}-\csc(x)+5
d
y
=
□
=
x
2
−
csc
(
x
)
+
5
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For the following equation, evaluate
f
′
(
1
)
f^{\prime}(1)
f
′
(
1
)
.
\newline
f
(
x
)
=
5
x
5
+
2
x
3
+
x
f(x)=5 x^{5}+2 x^{3}+x
f
(
x
)
=
5
x
5
+
2
x
3
+
x
\newline
Answer:
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For the following equation, evaluate
f
′
(
3
)
f^{\prime}(3)
f
′
(
3
)
.
\newline
f
(
x
)
=
−
x
3
−
4
x
f(x)=-x^{3}-4 x
f
(
x
)
=
−
x
3
−
4
x
\newline
Answer:
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For the following equation, find
d
y
d
x
\frac{d y}{d x}
d
x
d
y
.
\newline
y
=
4
x
5
+
4
x
−
7
y=4 x^{5}+4 x-7
y
=
4
x
5
+
4
x
−
7
\newline
Answer:
d
y
d
x
=
\frac{d y}{d x}=
d
x
d
y
=
Get tutor help
For the following equation, find
f
′
(
x
)
f^{\prime}(x)
f
′
(
x
)
.
\newline
f
(
x
)
=
7
x
5
+
5
f(x)=7 x^{5}+5
f
(
x
)
=
7
x
5
+
5
\newline
Answer:
f
′
(
x
)
=
f^{\prime}(x)=
f
′
(
x
)
=
Get tutor help
Given the function
\newline
y
=
4
(
9
x
2
−
8
x
)
6
5
y=4(9x^{2}-8x)^{\frac{6}{5}}
y
=
4
(
9
x
2
−
8
x
)
5
6
find
d
y
d
x
\frac{dy}{dx}
d
x
d
y
in any form.
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Given the function
\newline
f
(
x
)
=
(
−
9
x
−
5
)
1
3
,
f(x)=(-9x-5)^{\frac{1}{3}},
f
(
x
)
=
(
−
9
x
−
5
)
3
1
,
find
\newline
f
′
(
x
)
f'(x)
f
′
(
x
)
in any form.
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What is the inverse of the function
f
(
x
)
=
−
6
x
−
7
f(x) = -6x - 7
f
(
x
)
=
−
6
x
−
7
?
f
−
1
(
x
)
=
□
f^{-1}(x) = \square
f
−
1
(
x
)
=
□
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What is the inverse of the function
\newline
g
(
x
)
=
−
x
−
2
x
+
4
g(x) = \frac{-x - 2}{x + 4}
g
(
x
)
=
x
+
4
−
x
−
2
?
\newline
g
−
1
(
x
)
=
□
g^{-1}(x) = \square
g
−
1
(
x
)
=
□
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What is the inverse of the function
g
(
x
)
=
−
3
(
x
+
6
)
g(x) = -3(x+6)
g
(
x
)
=
−
3
(
x
+
6
)
?
g
−
1
(
x
)
=
□
g^{-1}(x) = \square
g
−
1
(
x
)
=
□
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What is the inverse of the function
h
(
x
)
=
3
−
x
x
+
1
h(x) = \frac{3-x}{x+1}
h
(
x
)
=
x
+
1
3
−
x
?
h
−
1
(
x
)
=
□
h^{-1}(x) = \square
h
−
1
(
x
)
=
□
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What is the inverse of the function
f
(
x
)
=
6
x
−
5
x
+
9
f(x) = \frac{6x - 5}{x + 9}
f
(
x
)
=
x
+
9
6
x
−
5
?
f
−
1
(
x
)
=
□
f^{-1}(x) = \square
f
−
1
(
x
)
=
□
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What is the inverse of the function
\newline
f
(
x
)
=
3
+
4
x
1
−
5
x
f(x) = \frac{3 + 4x}{1 - 5x}
f
(
x
)
=
1
−
5
x
3
+
4
x
?
\newline
f
−
1
(
x
)
=
□
f^{-1}(x) = \square
f
−
1
(
x
)
=
□
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