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What is $(f * g)(x)$ ? $\newline$ $f(x) = 4x + 1$ $\newline$ $g(x) = 2x$ $\newline$ Write your answer as a polynomial or a rational function in simplest form. $\newline$ ______

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Power rule with rational exponents

Full solution

Q. What is

(f * g)(x)

?

\newline

f(x) = 4x + 1

\newline

g(x) = 2x

\newline

Write your answer as a polynomial or a rational function in simplest form.

\newline

______

Multiply functions: To find the product $(f * g)(x)$ , we need to multiply the functions $f(x)$ and $g(x)$ together. $\newline$ $f(x) = 4x + 1$ $\newline$ $g(x) = 2x$ $\newline$ $(f * g)(x) = f(x) * g(x)$
Perform multiplication: Now we will perform the multiplication: $(f \cdot g)(x) = (4x + 1) \cdot (2x)$
Distribute $2x$ : Distribute $2x$ across the terms in the parentheses: $(f \cdot g)(x) = 4x \cdot 2x + 1 \cdot 2x$
Simplify multiplication: Simplify the multiplication: $(f \cdot g)(x) = 8x^2 + 2x$
Final answer: The expression $8x^2 + 2x$ is already in its simplest form, so this is our final answer.

More problems from Power rule with rational exponents

Question

h(x)=\log _{2}(x)

\newline

Can we use the mean value theorem to say the equation

h^{\prime}(x)=1

has a solution where

1<x<2

\newline

1

\newline

(A) No, since the function is not differentiable on that interval.

\newline

(B) No, since the average rate of change of

h

over the interval

1 \leq x \leq 2

1

\newline

(C) Yes, both conditions for using the mean value theorem have been met.

Posted 3 months ago

Question

What is the sign of

39 \frac{11}{13}+\left(-41 \frac{1}{13}\right) \text { ? }

\newline

1

\newline

\newline

\newline

(C) Neither positive nor negative-the sum is zero.

Posted 3 months ago

Question

What is the sign of

-1042+1042 ?

\newline

1

\newline

\newline

\newline

(C) Neither positive nor negative-the sum is zero.

Posted 3 months ago

Question

What is the sign of

-18 \frac{9}{17}+\left(-18 \frac{9}{17}\right)

\newline

1

\newline

\newline

\newline

(C) Neither positive nor negative-the sum is zero.

Posted 3 months ago

Question

What is the sign of

\frac{23}{45}+\left(-\frac{23}{45}\right) ?

\newline

1

\newline

\newline

\newline

(C) Neither positive nor negative-the sum is zero.

Posted 3 months ago

Question

What is the sign of

45+(-38)

\newline

1

\newline

\newline

\newline

(C) Neither positive nor negative-the sum is zero.

Posted 3 months ago

Question

What is the sign of

-49.8+61.2

\newline

1

\newline

\newline

\newline

(C) Neither positive nor negative-the sum is zero.

Posted 3 months ago

Question

What is the sign of

-1.69+(-1.69) ?

\newline

1

\newline

\newline

\newline

(C) Neither positive nor negative-the sum is zero.

Posted 3 months ago

Question

What is the sign of

37+(-37)

\newline

1

\newline

\newline

\newline

(C) Neither positive nor negative-the sum is zero.

Posted 3 months ago

Question

\begin{array}{l} g(x)=\sqrt{2 x-9} \\ g^{\prime}(x)=? \end{array}

\newline

1

\newline

\frac{\sqrt{2 x-9}}{2}

\newline

\frac{1}{\sqrt{2 x-9}}

\newline

\frac{1}{2 \sqrt{2 x-9}}

\newline

\frac{1}{\sqrt{x}}

Posted 3 months ago