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sider the following functions.

f(x)=-4x" and "g(x)=root(3)(x)
p 1 of 2 : Find the formula for
(f+g)(x) and simplify your answer. Then find the domain for
(f+g)(x). Round your answer to two decimal places, if necessa
Keyboard S-

(f+g)(x)=

" Domain "=

sider the following functions. $\newline$ $f(x)=-4 x \text { and } g(x)=\sqrt[3]{x}$ $\newline$ p $1$ of $2$ : Find the formula for $(f+g)(x)$ and simplify your answer. Then find the domain for $(f+g)(x)$ . Round your answer to two decimal places, if necessa $\newline$ Keyboard S- $\newline$ $(f+g)(x)=$ $\newline$ $\text { Domain }=$

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Write a formula for an arithmetic sequence

Full solution

Q. sider the following functions.

\newline

f(x)=-4 x \text { and } g(x)=\sqrt[3]{x}

\newline

p

1

of

2

: Find the formula for

(f+g)(x)

and simplify your answer. Then find the domain for

(f+g)(x)

. Round your answer to two decimal places, if necessa

\newline

Keyboard S-

\newline

(f+g)(x)=

\newline

\text { Domain }=

Define Functions: To find the formula for $(f+g)(x)$ , we need to add the functions $f(x)$ and $g(x)$ together. The function $f(x)$ is given as $-4x$ , and $g(x)$ is given as the cube root of $x$ , which can be written as $x^{1/3}$ .
Calculate Sum: The sum of the functions $(f+g)(x)$ is found by adding $f(x)$ and $g(x)$ together: $(f+g)(x) = f(x) + g(x) = -4x + x^{1/3}$ .
Simplify Expression: The expression for $(f+g)(x)$ cannot be simplified further because the terms involve $x$ raised to different powers, and these terms are not like terms. Therefore, the simplified expression for $(f+g)(x)$ is $(f+g)(x) = -4x + x^{(1/3)}.$
Find Domain: To find the domain of $(f+g)(x)$ , we need to consider the domains of both $f(x)$ and $g(x)$ individually. The domain of $f(x) = -4x$ is all real numbers because there are no restrictions on $x$ for a linear function. The domain of $g(x) = x^{1/3}$ is also all real numbers because the cube root function is defined for all real numbers, including negative numbers.
Determine Domain: Since both $f(x)$ and $g(x)$ have the domain of all real numbers, the domain of $(f+g)(x)$ is also all real numbers. There is no need to round the domain since it is not a numerical value but rather a set of all real numbers.

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