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Determine whether the function
f(x)=-7x^(3)+x^(5) is even, odd or neither.
neither
odd
even

Determine whether the function $f(x)=-7 x^{3}+x^{5}$ is even, odd or neither. $\newline$ neither $\newline$ odd $\newline$ even

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Even and odd functions

Full solution

Q. Determine whether the function

f(x)=-7 x^{3}+x^{5}

is even, odd or neither.

\newline

neither

\newline

odd

\newline

even

Define $f(x)$ : Define the function $f(x)$ . The given function is $f(x) = -7x^{3} + x^{5}$ . 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 $f(-x)$ . $\newline$ $f(-x) = -7(-x)^{3} + (-x)^{5}$ $\newline$ $f(-x) = -7(-x^3) + (-x^5)$ $\newline$ $f(-x) = 7x^3 - x^5$
Compare $f(x)$ with $f(-x)$ : Compare $f(x)$ with $f(-x)$ . We have $f(x) = -7x^3 + x^5$ and $f(-x) = 7x^3 - x^5$ . 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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