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Welcome to Bytelearn!
Let’s check out your problem:
Given the functions
f
(
x
)
=
4
x
3
f(x)=4 x^{3}
f
(
x
)
=
4
x
3
and
g
(
x
)
=
4
⋅
3
x
g(x)=4 \cdot 3^{x}
g
(
x
)
=
4
⋅
3
x
, which of the following statements is true?
\newline
f
(
3
)
=
g
(
3
)
f(3)=g(3)
f
(
3
)
=
g
(
3
)
\newline
f
(
3
)
>
g
(
3
)
f(3)>g(3)
f
(
3
)
>
g
(
3
)
\newline
f
(
3
)
<
g
(
3
)
f(3)<g(3)
f
(
3
)
<
g
(
3
)
View step-by-step help
Home
Math Problems
Algebra 1
Properties of matrices
Full solution
Q.
Given the functions
f
(
x
)
=
4
x
3
f(x)=4 x^{3}
f
(
x
)
=
4
x
3
and
g
(
x
)
=
4
⋅
3
x
g(x)=4 \cdot 3^{x}
g
(
x
)
=
4
⋅
3
x
, which of the following statements is true?
\newline
f
(
3
)
=
g
(
3
)
f(3)=g(3)
f
(
3
)
=
g
(
3
)
\newline
f
(
3
)
>
g
(
3
)
f(3)>g(3)
f
(
3
)
>
g
(
3
)
\newline
f
(
3
)
<
g
(
3
)
f(3)<g(3)
f
(
3
)
<
g
(
3
)
Calculate
f
(
3
)
f(3)
f
(
3
)
:
Calculate
f
(
3
)
f(3)
f
(
3
)
using the function
f
(
x
)
=
4
x
3
f(x)=4x^{3}
f
(
x
)
=
4
x
3
.
f
(
3
)
=
4
×
3
3
=
4
×
27
=
108
f(3) = 4 \times 3^{3} = 4 \times 27 = 108
f
(
3
)
=
4
×
3
3
=
4
×
27
=
108
Calculate
g
(
3
)
g(3)
g
(
3
)
:
Calculate
g
(
3
)
g(3)
g
(
3
)
using the function
g
(
x
)
=
4
⋅
3
x
g(x)=4\cdot3^{x}
g
(
x
)
=
4
⋅
3
x
.
g
(
3
)
=
4
⋅
3
3
=
4
⋅
27
=
108
g(3) = 4 \cdot 3^{3} = 4 \cdot 27 = 108
g
(
3
)
=
4
⋅
3
3
=
4
⋅
27
=
108
Compare values:
Compare the values of
f
(
3
)
f(3)
f
(
3
)
and
g
(
3
)
g(3)
g
(
3
)
.
\newline
Since
f
(
3
)
=
108
f(3) = 108
f
(
3
)
=
108
and
g
(
3
)
=
108
g(3) = 108
g
(
3
)
=
108
, we have
f
(
3
)
=
g
(
3
)
f(3) = g(3)
f
(
3
)
=
g
(
3
)
.
More problems from Properties of matrices
Question
Is this an identity matrix?
\newline
[
0
11
0
]
\begin{bmatrix} 0 & 1 1 & 0 \end{bmatrix}
[
0
11
0
]
\newline
Choices:
\newline
yes
\text{yes}
yes
\newline
no
\text{no}
no
Get tutor help
Posted 1 month ago
Question
Consider this matrix transformation:
\newline
[
2
3
−
3
−
1
]
\left[\begin{array}{cc} 2 & 3 \\ & \\ -3 & -1 \end{array}\right]
⎣
⎡
2
−
3
3
−
1
⎦
⎤
\newline
What is the image of
[
4
1
]
\left[\begin{array}{l}4 \\ 1\end{array}\right]
[
4
1
]
under this transformation?
Get tutor help
Posted 2 months ago
Question
Answer the following True or False.
\newline
Since
d
d
x
3
x
1
3
=
x
−
2
3
\frac{d}{dx}3x^{\frac{1}{3}}=x^{-\frac{2}{3}}
d
x
d
3
x
3
1
=
x
−
3
2
, the fundamental theorem of calculus tells us that
∫
−
1
1
x
−
2
3
d
x
=
3
(
1
1
3
)
−
3
(
−
1
)
1
3
=
6
\int_{-1}^{1}x^{-\frac{2}{3}}dx=3(1^{\frac{1}{3}})-3(-1)^{\frac{1}{3}}=6
∫
−
1
1
x
−
3
2
d
x
=
3
(
1
3
1
)
−
3
(
−
1
)
3
1
=
6
.
\newline
True
\newline
False
Get tutor help
Posted 2 months ago
Question
Answer the following True or False.
\newline
∫
3
x
d
x
=
3
x
+
C
ln
3
\int 3^{x}\,dx = \frac{3^{x} + C}{\ln 3}
∫
3
x
d
x
=
l
n
3
3
x
+
C
\newline
True
\newline
False
Get tutor help
Posted 2 months ago
Question
Answer the following True or False.
\newline
∫
1
sec
x
d
x
=
ln
(
sec
x
)
+
C
\int \frac{1}{\sec x}\,dx = \ln(\sec x) + C
∫
s
e
c
x
1
d
x
=
ln
(
sec
x
)
+
C
\newline
True
\newline
False
Get tutor help
Posted 2 months ago
Question
Answer the following True or False.
\newline
Suppose
a
a
a
and
b
b
b
are both positive real numbers. Then
∫
a
b
1
x
2
d
x
=
∫
−
b
−
a
1
x
2
d
x
.
\int_{a}^{b}\frac{1}{x^{2}}dx=\int_{-b}^{-a}\frac{1}{x^{2}}dx.
∫
a
b
x
2
1
d
x
=
∫
−
b
−
a
x
2
1
d
x
.
\newline
True
\newline
False
\newline
Next Question
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Posted 2 months ago
Question
Answer the following True or False.
\newline
∫
−
a
a
(
3
x
3
+
9
x
)
d
x
=
0
\int_{-a}^{a}(3x^{3}+9x)dx=0
∫
−
a
a
(
3
x
3
+
9
x
)
d
x
=
0
\newline
True
\newline
False
Get tutor help
Posted 2 months ago
Question
What value of
x
x
x
makes the equation below true?
\newline
10
x
+
8
=
78
10 x+8=78
10
x
+
8
=
78
\newline
4
4
4
\newline
7
7
7
\newline
8
8
8
\newline
9
9
9
Get tutor help
Posted 2 months ago
Question
Answer the following True or False. For all
1
<
a
<
b
1 < a < b
1
<
a
<
b
,
∫
a
b
x
2
d
x
>
∫
a
b
x
d
x
\int_{a}^{b} x^{2} \, dx > \int_{a}^{b} x \, dx
∫
a
b
x
2
d
x
>
∫
a
b
x
d
x
.
\newline
True
\newline
False
Get tutor help
Posted 2 months ago
Question
Answer the following True or False.
\newline
∫
8
x
d
x
=
8
x
+
C
ln
8
\int 8^x \, dx = \frac{8^x + C}{\ln 8}
∫
8
x
d
x
=
l
n
8
8
x
+
C
\newline
True
\newline
False
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Posted 2 months ago