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Welcome to Bytelearn!
Let’s check out your problem:
What is
(
f
∗
g
)
(
x
)
(f * g)(x)
(
f
∗
g
)
(
x
)
?
\newline
f
(
x
)
=
4
x
+
1
f(x) = 4x + 1
f
(
x
)
=
4
x
+
1
\newline
g
(
x
)
=
3
x
g(x) = 3x
g
(
x
)
=
3
x
\newline
Write your answer as a polynomial or a rational function in simplest form.
\newline
______
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Home
Math Problems
Algebra 1
Power rule with rational exponents
Full solution
Q.
What is
(
f
∗
g
)
(
x
)
(f * g)(x)
(
f
∗
g
)
(
x
)
?
\newline
f
(
x
)
=
4
x
+
1
f(x) = 4x + 1
f
(
x
)
=
4
x
+
1
\newline
g
(
x
)
=
3
x
g(x) = 3x
g
(
x
)
=
3
x
\newline
Write your answer as a polynomial or a rational function in simplest form.
\newline
______
Multiply functions:
To find the product
(
f
∗
g
)
(
x
)
(f * g)(x)
(
f
∗
g
)
(
x
)
, we need to multiply the functions
f
(
x
)
f(x)
f
(
x
)
and
g
(
x
)
g(x)
g
(
x
)
together.
\newline
f
(
x
)
=
4
x
+
1
f(x) = 4x + 1
f
(
x
)
=
4
x
+
1
\newline
g
(
x
)
=
3
x
g(x) = 3x
g
(
x
)
=
3
x
\newline
(
f
∗
g
)
(
x
)
=
f
(
x
)
∗
g
(
x
)
(f * g)(x) = f(x) * g(x)
(
f
∗
g
)
(
x
)
=
f
(
x
)
∗
g
(
x
)
Perform multiplication:
Now we will perform the multiplication:
\newline
(
f
⋅
g
)
(
x
)
=
(
4
x
+
1
)
⋅
(
3
x
)
(f \cdot g)(x) = (4x + 1) \cdot (3x)
(
f
⋅
g
)
(
x
)
=
(
4
x
+
1
)
⋅
(
3
x
)
Distribute
3
x
3x
3
x
:
Distribute
3
x
3x
3
x
across the terms in the parentheses:
(
f
⋅
g
)
(
x
)
=
4
x
⋅
3
x
+
1
⋅
3
x
(f \cdot g)(x) = 4x \cdot 3x + 1 \cdot 3x
(
f
⋅
g
)
(
x
)
=
4
x
⋅
3
x
+
1
⋅
3
x
Simplify multiplication:
Simplify the multiplication:
(
f
⋅
g
)
(
x
)
=
12
x
2
+
3
x
(f \cdot g)(x) = 12x^2 + 3x
(
f
⋅
g
)
(
x
)
=
12
x
2
+
3
x
More problems from Power rule with rational exponents
Question
Let
h
(
x
)
=
log
2
(
x
)
h(x)=\log _{2}(x)
h
(
x
)
=
lo
g
2
(
x
)
.
\newline
Can we use the mean value theorem to say the equation
h
′
(
x
)
=
1
h^{\prime}(x)=1
h
′
(
x
)
=
1
has a solution where
1
<
x
<
2
1<x<2
1
<
x
<
2
?
\newline
Choose
1
1
1
answer:
\newline
(A) No, since the function is not differentiable on that interval.
\newline
(B) No, since the average rate of change of
h
h
h
over the interval
1
≤
x
≤
2
1 \leq x \leq 2
1
≤
x
≤
2
isn't equal to
1
1
1
.
\newline
(C) Yes, both conditions for using the mean value theorem have been met.
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Posted 9 months ago
Question
What is the sign of
39
11
13
+
(
−
41
1
13
)
?
39 \frac{11}{13}+\left(-41 \frac{1}{13}\right) \text { ? }
39
13
11
+
(
−
41
13
1
)
?
\newline
Choose
1
1
1
answer:
\newline
(A) Positive
\newline
(B) Negative
\newline
(C) Neither positive nor negative-the sum is zero.
Get tutor help
Posted 9 months ago
Question
What is the sign of
−
1042
+
1042
?
-1042+1042 ?
−
1042
+
1042
?
\newline
Choose
1
1
1
answer:
\newline
(A) Positive
\newline
(B) Negative
\newline
(C) Neither positive nor negative-the sum is zero.
Get tutor help
Posted 9 months ago
Question
What is the sign of
−
18
9
17
+
(
−
18
9
17
)
-18 \frac{9}{17}+\left(-18 \frac{9}{17}\right)
−
18
17
9
+
(
−
18
17
9
)
?
\newline
Choose
1
1
1
answer:
\newline
(A) Positive
\newline
(B) Negative
\newline
(C) Neither positive nor negative-the sum is zero.
Get tutor help
Posted 9 months ago
Question
What is the sign of
23
45
+
(
−
23
45
)
?
\frac{23}{45}+\left(-\frac{23}{45}\right) ?
45
23
+
(
−
45
23
)
?
\newline
Choose
1
1
1
answer:
\newline
(A) Positive
\newline
(B) Negative
\newline
(C) Neither positive nor negative-the sum is zero.
Get tutor help
Posted 9 months ago
Question
What is the sign of
45
+
(
−
38
)
45+(-38)
45
+
(
−
38
)
?
\newline
Choose
1
1
1
answer:
\newline
(A) Positive
\newline
(B) Negative
\newline
(C) Neither positive nor negative-the sum is zero.
Get tutor help
Posted 9 months ago
Question
What is the sign of
−
49.8
+
61.2
-49.8+61.2
−
49.8
+
61.2
?
\newline
Choose
1
1
1
answer:
\newline
(A) Positive
\newline
(B) Negative
\newline
(C) Neither positive nor negative-the sum is zero.
Get tutor help
Posted 9 months ago
Question
What is the sign of
−
1.69
+
(
−
1.69
)
?
-1.69+(-1.69) ?
−
1.69
+
(
−
1.69
)?
\newline
Choose
1
1
1
answer:
\newline
(A) Positive
\newline
(B) Negative
\newline
(C) Neither positive nor negative-the sum is zero.
Get tutor help
Posted 9 months ago
Question
What is the sign of
37
+
(
−
37
)
37+(-37)
37
+
(
−
37
)
?
\newline
Choose
1
1
1
answer:
\newline
(A) Positive
\newline
(B) Negative
\newline
(C) Neither positive nor negative-the sum is zero.
Get tutor help
Posted 9 months ago
Question
g
(
x
)
=
2
x
−
9
g
′
(
x
)
=
?
\begin{array}{l} g(x)=\sqrt{2 x-9} \\ g^{\prime}(x)=? \end{array}
g
(
x
)
=
2
x
−
9
g
′
(
x
)
=
?
\newline
Choose
1
1
1
answer:
\newline
(A)
2
x
−
9
2
\frac{\sqrt{2 x-9}}{2}
2
2
x
−
9
\newline
(B)
1
2
x
−
9
\frac{1}{\sqrt{2 x-9}}
2
x
−
9
1
\newline
(C)
1
2
2
x
−
9
\frac{1}{2 \sqrt{2 x-9}}
2
2
x
−
9
1
\newline
(D)
1
x
\frac{1}{\sqrt{x}}
x
1
Get tutor help
Posted 9 months ago
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