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What is $(f * g)(x)$ ? $\newline$ $f(x) = -2x + 4$ $\newline$ $g(x) = -2x$ $\newline$ 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) = -2x + 4

\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 of two functions, $f(x)$ and $g(x)$ , we multiply them together. This is denoted as $(f * g)(x)$ and means we need to multiply $f(x)$ by $g(x)$ . $\newline$ $f(x) = -2x + 4$ $\newline$ $g(x) = -2x$ $\newline$ $(f * g)(x) = f(x) * g(x)$
Perform Multiplication: Now we will perform the multiplication: $\newline$ $(f * g)(x) = (-2x + 4) * (-2x)$ $\newline$ To multiply these two expressions, we use the distributive property $(a(b + c) = ab + ac)$ .
Distribute $-2x$ : We distribute $-2x$ across the terms in the parentheses: $\newline$ (f \cdot g)(x) = \(-2x \cdot ( $-2$ x) + ( $-2$ x) \cdot $4$
Calculate Each Term: Now we calculate each term: $\newline$ $-2x \times (-2x) = 4x^2$ (since a negative times a negative is a positive) $\newline$ $(-2x) \times 4 = -8x$ $\newline$ So, $(f \times g)(x) = 4x^2 - 8x$

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

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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

\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

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What is the sign of

45+(-38)

\newline

1

\newline

\newline

\newline

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

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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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What is the sign of

-1.69+(-1.69) ?

\newline

1

\newline

\newline

\newline

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

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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