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Determine whether the function
f(x)=-7x^(3)-x^(4) is even, odd or neither.
even
odd
neither

Determine whether the function $f(x)=-7 x^{3}-x^{4}$ is even, odd or neither. $\newline$ even $\newline$ odd $\newline$ neither

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Even and odd functions

Full solution

Q. Determine whether the function

f(x)=-7 x^{3}-x^{4}

is even, odd or neither.

\newline

even

\newline

odd

\newline

neither

Define $f(x)$ : Define the function $f(x)$ . The given function is $f(x) = -7x^{3} - x^{4}$ . To determine if the function is even, odd, or neither, we need to compare $f(x)$ with $f(-x)$ .
Calculate $f(-x)$ : Calculate $f(-x)$ . $\newline$ Substitute $-x$ for $x$ in $f(x)$ to get $f(-x)$ . $\newline$ $f(-x)=-7(-x)^{3}-(-x)^{4}$ $\newline$ $f(-x)=-7(-x^3)-x^4$
Simplify $f(-x)$ : Simplify $f(-x)$ . Simplify the expression for $f(-x)$ . $f(-x)=-7(-x^3)-x^4$ $f(-x)=7x^3-x^4$
Compare $f(x)$ with $f(-x)$ : Compare $f(x)$ with $f(-x)$ . We have $f(x)=-7x^{3}-x^{4}$ and $f(-x)=7x^{3}-x^{4}$ . Since $f(-x)$ is not equal to $f(x)$ and $f(-x)$ is not equal to $-f(x)$ , the function is neither even nor odd.

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