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Determine whether the function
f(x)=-2x^(4)+x^(5) is even, odd or neither.
odd
even
neither

Determine whether the function $f(x)=-2 x^{4}+x^{5}$ is even, odd or neither. $\newline$ odd $\newline$ even $\newline$ neither

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Even and odd functions

Full solution

Q. Determine whether the function

f(x)=-2 x^{4}+x^{5}

is even, odd or neither.

\newline

odd

\newline

even

\newline

neither

Evaluate $f(-x)$ : To determine if the function is even, odd, or neither, we need to evaluate $f(-x)$ and compare it to $f(x)$ . If $f(-x) = f(x)$ , the function is even. If $f(-x) = -f(x)$ , the function is odd. If neither condition is met, the function is neither even nor odd. $\newline$ Let's start by finding $f(-x)$ . $\newline$ $f(-x) = -2(-x)^{4} + (-x)^{5}$
Simplify $f(-x)$ : Now we simplify the expression for $f(-x)$ . $f(-x) = -2(x^4) - x^5$
Compare $f(-x)$ with $f(x)$ : Next, we compare $f(-x)$ with $f(x)$ . We have $f(x) = -2x^4 + x^5$ and $f(-x) = -2x^4 - x^5$ . 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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