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Math Problems
Algebra 2
Find the vertex of the transformed function
What is the inverse of the function
g
(
x
)
=
9
x
+
4
x
−
7
g(x) = \frac{9x + 4}{x - 7}
g
(
x
)
=
x
−
7
9
x
+
4
?
g
−
1
(
x
)
=
□
g^{-1}(x) = \square
g
−
1
(
x
)
=
□
Get tutor help
What is the inverse of the function
f
(
x
)
=
−
2
x
+
2
x
+
7
f(x)=\frac{-2x+2}{x+7}
f
(
x
)
=
x
+
7
−
2
x
+
2
?
f
−
1
(
x
)
=
□
f^{-1}(x)=\square
f
−
1
(
x
)
=
□
Get tutor help
y
=
x
2
tan
(
x
)
y=x^{2}\tan(x)
y
=
x
2
tan
(
x
)
\newline
d
y
d
x
=
\frac{dy}{dx}=
d
x
d
y
=
Get tutor help
Given the function
f
(
x
)
=
4
(
−
4
x
2
−
3
x
−
5
)
3
f(x)=4\left(-4 x^{2}-3 x-5\right)^{3}
f
(
x
)
=
4
(
−
4
x
2
−
3
x
−
5
)
3
, find
f
′
(
x
)
f^{\prime}(x)
f
′
(
x
)
in any form.
\newline
Answer:
f
′
(
x
)
=
f^{\prime}(x)=
f
′
(
x
)
=
Get tutor help
Given the function
f
(
x
)
=
−
2
(
−
8
x
−
5
)
5
f(x)=-2(-8 x-5)^{5}
f
(
x
)
=
−
2
(
−
8
x
−
5
)
5
, find
f
′
(
x
)
f^{\prime}(x)
f
′
(
x
)
in any form.
\newline
Answer:
f
′
(
x
)
=
f^{\prime}(x)=
f
′
(
x
)
=
Get tutor help
Given the function
f
(
x
)
=
−
2
(
−
8
x
2
−
2
)
4
f(x)=-2\left(-8 x^{2}-2\right)^{4}
f
(
x
)
=
−
2
(
−
8
x
2
−
2
)
4
, find
f
′
(
x
)
f^{\prime}(x)
f
′
(
x
)
in any form.
\newline
Answer:
f
′
(
x
)
=
f^{\prime}(x)=
f
′
(
x
)
=
Get tutor help
Given the function
f
(
x
)
=
−
5
(
5
x
2
+
9
x
)
6
f(x)=-5\left(5 x^{2}+9 x\right)^{6}
f
(
x
)
=
−
5
(
5
x
2
+
9
x
)
6
, find
f
′
(
x
)
f^{\prime}(x)
f
′
(
x
)
in any form.
\newline
Answer:
f
′
(
x
)
=
f^{\prime}(x)=
f
′
(
x
)
=
Get tutor help
Given the function
f
(
x
)
=
(
x
2
−
8
x
+
9
)
5
f(x)=\left(x^{2}-8 x+9\right)^{5}
f
(
x
)
=
(
x
2
−
8
x
+
9
)
5
, find
f
′
(
x
)
f^{\prime}(x)
f
′
(
x
)
in any form.
\newline
Answer:
f
′
(
x
)
=
f^{\prime}(x)=
f
′
(
x
)
=
Get tutor help
Given the function
f
(
x
)
=
(
−
x
2
−
8
x
−
8
)
5
f(x)=\left(-x^{2}-8 x-8\right)^{5}
f
(
x
)
=
(
−
x
2
−
8
x
−
8
)
5
, find
f
′
(
x
)
f^{\prime}(x)
f
′
(
x
)
in any form.
\newline
Answer:
f
′
(
x
)
=
f^{\prime}(x)=
f
′
(
x
)
=
Get tutor help
Given the function
f
(
x
)
=
(
7
x
2
+
2
x
+
5
)
6
f(x)=\left(7 x^{2}+2 x+5\right)^{6}
f
(
x
)
=
(
7
x
2
+
2
x
+
5
)
6
, find
f
′
(
x
)
f^{\prime}(x)
f
′
(
x
)
in any form.
\newline
Answer:
f
′
(
x
)
=
f^{\prime}(x)=
f
′
(
x
)
=
Get tutor help
Given the function
f
(
x
)
=
(
8
x
−
6
)
6
f(x)=(8 x-6)^{6}
f
(
x
)
=
(
8
x
−
6
)
6
, find
f
′
(
x
)
f^{\prime}(x)
f
′
(
x
)
in any form.
\newline
Answer:
f
′
(
x
)
=
f^{\prime}(x)=
f
′
(
x
)
=
Get tutor help
Given the function
y
=
(
−
x
2
−
5
x
)
3
y=\left(-x^{2}-5 x\right)^{3}
y
=
(
−
x
2
−
5
x
)
3
, find
d
y
d
x
\frac{d y}{d x}
d
x
d
y
in any form.
\newline
Answer:
d
y
d
x
=
\frac{d y}{d x}=
d
x
d
y
=
Get tutor help
Given the function
f
(
x
)
=
(
−
2
x
2
+
6
x
)
6
f(x)=\left(-2 x^{2}+6 x\right)^{6}
f
(
x
)
=
(
−
2
x
2
+
6
x
)
6
, find
f
′
(
x
)
f^{\prime}(x)
f
′
(
x
)
in any form.
\newline
Answer:
f
′
(
x
)
=
f^{\prime}(x)=
f
′
(
x
)
=
Get tutor help
Given the function
f
(
x
)
=
−
3
(
4
x
2
−
7
x
)
5
f(x)=-3\left(4 x^{2}-7 x\right)^{5}
f
(
x
)
=
−
3
(
4
x
2
−
7
x
)
5
, find
f
′
(
x
)
f^{\prime}(x)
f
′
(
x
)
in any form.
\newline
Answer:
f
′
(
x
)
=
f^{\prime}(x)=
f
′
(
x
)
=
Get tutor help
Given the function
f
(
x
)
=
2
(
−
9
x
2
+
x
+
6
)
4
f(x)=2\left(-9 x^{2}+x+6\right)^{4}
f
(
x
)
=
2
(
−
9
x
2
+
x
+
6
)
4
, find
f
′
(
x
)
f^{\prime}(x)
f
′
(
x
)
in any form.
\newline
Answer:
f
′
(
x
)
=
f^{\prime}(x)=
f
′
(
x
)
=
Get tutor help
A curve is defined by the parametric equations
x
(
t
)
=
7
t
3
x(t)=7 t^{3}
x
(
t
)
=
7
t
3
and
y
(
t
)
=
t
2
−
2
t
−
5
y(t)=t^{2}-2 t-5
y
(
t
)
=
t
2
−
2
t
−
5
. Find
d
y
d
x
\frac{d y}{d x}
d
x
d
y
.
\newline
Answer:
Get tutor help
A curve is defined by the parametric equations
x
(
t
)
=
7
t
3
−
t
x(t)=7 t^{3}-t
x
(
t
)
=
7
t
3
−
t
and
y
(
t
)
=
−
9
sin
(
−
2
t
)
y(t)=-9 \sin (-2 t)
y
(
t
)
=
−
9
sin
(
−
2
t
)
. Find
d
y
d
x
\frac{d y}{d x}
d
x
d
y
.
\newline
Answer:
Get tutor help
Decompose the function
f
(
g
(
h
(
x
)
)
)
=
3
(
cos
x
+
6
)
f(g(h(x)))=3^{(\cos x+6)}
f
(
g
(
h
(
x
)))
=
3
(
c
o
s
x
+
6
)
into
f
(
x
)
f(x)
f
(
x
)
,
g
(
x
)
g(x)
g
(
x
)
and
h
(
x
)
h(x)
h
(
x
)
.
Get tutor help
What is the inverse of the function
h
(
x
)
=
3
2
(
x
−
11
)
?
h(x)=\frac{3}{2}(x-11)?
h
(
x
)
=
2
3
(
x
−
11
)?
\newline
h
−
1
(
x
)
=
□
h^{-1}(x)=\square
h
−
1
(
x
)
=
□
Get tutor help
What is the inverse of the function
g
(
x
)
=
7
x
+
3
x
−
5
g(x) = \frac{7x+3}{x-5}
g
(
x
)
=
x
−
5
7
x
+
3
?
\newline
g
−
1
(
x
)
=
□
g^{-1}(x) = \square
g
−
1
(
x
)
=
□
Get tutor help
What is the inverse of the function
h
(
x
)
=
3
4
x
+
12
h(x)=\frac{3}{4}x+12
h
(
x
)
=
4
3
x
+
12
?
\newline
h
−
1
(
x
)
=
□
h^{-1}(x)=\square
h
−
1
(
x
)
=
□
Get tutor help
Given the function
f
(
x
)
=
6
−
x
1
+
x
3
f(x)=\frac{6-x}{1+x^{3}}
f
(
x
)
=
1
+
x
3
6
−
x
, find
f
′
(
x
)
f^{\prime}(x)
f
′
(
x
)
in simplified form.
\newline
Answer:
f
′
(
x
)
=
f^{\prime}(x)=
f
′
(
x
)
=
Get tutor help
Given the function
f
(
x
)
=
x
5
−
2
x
4
f(x)=\frac{x}{5-2 x^{4}}
f
(
x
)
=
5
−
2
x
4
x
, find
f
′
(
x
)
f^{\prime}(x)
f
′
(
x
)
in simplified form.
\newline
Answer:
f
′
(
x
)
=
f^{\prime}(x)=
f
′
(
x
)
=
Get tutor help
Given the function
f
(
x
)
=
5
−
x
x
3
+
5
f(x)=\frac{5-x}{x^{3}+5}
f
(
x
)
=
x
3
+
5
5
−
x
, find
f
′
(
x
)
f^{\prime}(x)
f
′
(
x
)
in simplified form.
\newline
Answer:
f
′
(
x
)
=
f^{\prime}(x)=
f
′
(
x
)
=
Get tutor help
Given the function
f
(
x
)
=
x
5
−
4
x
4
f(x)=\frac{x}{5-4 x^{4}}
f
(
x
)
=
5
−
4
x
4
x
, find
f
′
(
x
)
f^{\prime}(x)
f
′
(
x
)
in simplified form.
\newline
Answer:
f
′
(
x
)
=
f^{\prime}(x)=
f
′
(
x
)
=
Get tutor help
h
(
x
)
=
x
8
h(x)=x^{8}
h
(
x
)
=
x
8
\newline
h
′
(
x
)
=
h^{\prime}(x)=
h
′
(
x
)
=
Get tutor help
If
f
′
(
x
)
=
f
(
x
)
f^{\prime}(x)=f(x)
f
′
(
x
)
=
f
(
x
)
and
f
(
3
)
=
e
2
f(3)=e^{2}
f
(
3
)
=
e
2
, then
f
(
4
)
=
m
e
n
f(4)=m e^{n}
f
(
4
)
=
m
e
n
for some integers
m
m
m
and
n
n
n
.
\newline
What are
m
m
m
and
n
n
n
?
\newline
m
=
□
n
=
□
\begin{array}{l} m= \square \\ n= \square \end{array}
m
=
□
n
=
□
Get tutor help
f
′
(
x
)
=
9
e
x
and
f
(
8
)
=
−
8
+
9
e
8
.
f
(
0
)
=
□
\begin{array}{l}f^{\prime}(x)=9 e^{x} \text { and } f(8)=-8+9 e^{8} . \\ f(0)=\square\end{array}
f
′
(
x
)
=
9
e
x
and
f
(
8
)
=
−
8
+
9
e
8
.
f
(
0
)
=
□
Get tutor help
y
=
x
7
d
y
d
x
=
\begin{array}{c}y=x^{7} \\ \frac{d y}{d x}=\end{array}
y
=
x
7
d
x
d
y
=
Get tutor help
- Let
g
g
g
be a function such that
g
(
1
)
=
5
g(1)=5
g
(
1
)
=
5
and
g
′
(
1
)
=
−
3
g^{\prime}(1)=-3
g
′
(
1
)
=
−
3
.
\newline
- Let
h
h
h
be the function
h
(
x
)
=
x
2
h(x)=x^{2}
h
(
x
)
=
x
2
.
\newline
Let
F
F
F
be a function defined as
F
(
x
)
=
g
(
x
)
h
(
x
)
F(x)=\frac{g(x)}{h(x)}
F
(
x
)
=
h
(
x
)
g
(
x
)
.
\newline
F
′
(
1
)
=
F^{\prime}(1)=
F
′
(
1
)
=
Get tutor help
Consider the curve given by the equation
y
3
−
x
y
=
2
y^{3}-x y=2
y
3
−
x
y
=
2
. It can be shown that
d
y
d
x
=
y
3
y
2
−
x
\frac{d y}{d x}=\frac{y}{3 y^{2}-x}
d
x
d
y
=
3
y
2
−
x
y
.
\newline
Find the point on the curve where the line tangent to the curve is vertical.
\newline
(
□
(\square
(
□
,
□
)
\square)
□
)
Get tutor help
We are given that
d
y
d
x
=
e
5
y
\frac{d y}{d x}=e^{5 y}
d
x
d
y
=
e
5
y
.
\newline
Find an expression for
d
2
y
d
x
2
\frac{d^{2} y}{d x^{2}}
d
x
2
d
2
y
in terms of
x
x
x
and
y
y
y
.
\newline
d
2
y
d
x
2
=
\frac{d^{2} y}{d x^{2}}=
d
x
2
d
2
y
=
Get tutor help
We are given that
d
y
d
x
=
x
2
−
2
y
\frac{d y}{d x}=x^{2}-2 y
d
x
d
y
=
x
2
−
2
y
.
\newline
Find an expression for
d
2
y
d
x
2
\frac{d^{2} y}{d x^{2}}
d
x
2
d
2
y
in terms of
x
x
x
and
y
y
y
.
\newline
d
2
y
d
x
2
=
\frac{d^{2} y}{d x^{2}}=
d
x
2
d
2
y
=
Get tutor help
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