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Determine whether the function
f(x)=6x^(5)-x^(2) is even, odd or neither.
even
neither
odd

Determine whether the function $f(x)=6 x^{5}-x^{2}$ is even, odd or neither. $\newline$ even $\newline$ neither $\newline$ odd

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Even and odd functions

Full solution

Q. Determine whether the function

f(x)=6 x^{5}-x^{2}

is even, odd or neither.

\newline

even

\newline

neither

\newline

odd

Define function $f(x)$ : Define the function $f(x)$ . The given function is $f(x) = 6x^{5} - x^{2}$ . 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 $f(x)=6x^{5}-x^{2}$ to get $f(-x)$ . $\newline$ $f(-x)=6(-x)^{5}-(-x)^{2}$
Simplify $f(-x)$ : Simplify $f(-x)$ . Simplify the expression for $f(-x)$ by evaluating the powers of $-x$ . $f(-x)=6(-1)^5x^{5}-(-1)^2x^{2}$ $f(-x)=-6x^{5}-x^{2}$
Compare $f(x)$ with $f(-x)$ : Compare $f(x)$ with $f(-x)$ . We have $f(x)=6x^{5}-x^{2}$ and $f(-x)=-6x^{5}-x^{2}$ . 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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