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What is $(f * g)(x)$ ? $\newline$ $f(x) = 3x + 3$ $\newline$ $g(x) = -3x$ $\newline$ 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) = 3x + 3

\newline

g(x) = -3x

\newline

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

\newline

______

Multiply Functions: To find the product of two functions, $f(x)$ and $g(x)$ , we multiply them together. We have $f(x) = 3x + 3$ and $g(x) = -3x$ . Now, we will multiply $f(x)$ by $g(x)$ . $(f * g)(x) = f(x) * g(x)$ $(f * g)(x) = (3x + 3) * (-3x)$
Distribute $-3x$ : Distribute the $-3x$ across the terms in the parentheses. $\newline$ $(f \cdot g)(x) = 3x \cdot (-3x) + 3 \cdot (-3x)$
Perform Multiplication: Perform the multiplication for each term. $\newline$ $(f * g)(x) = -9x^2 - 9x$
Final Answer: The expression is already simplified and there are no like terms to combine. $\newline$ So, the final answer is $(f * g)(x) = -9x^2 - 9x$ .

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.

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What is the sign of

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

\newline

1

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\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

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\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.

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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

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\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