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Determine whether the function
f(x)=-5x^(4)-1-5x^(6) is even, odd or neither.
odd
neither
even

Determine whether the function $f(x)=-5 x^{4}-1-5 x^{6}$ is even, odd or neither. $\newline$ odd $\newline$ neither $\newline$ even

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Even and odd functions

Full solution

Q. Determine whether the function

f(x)=-5 x^{4}-1-5 x^{6}

is even, odd or neither.

\newline

odd

\newline

neither

\newline

even

Define function $f(x)$ : Define the function $f(x)$ . The given function is $f(x) = -5x^{4} - 1 - 5x^{6}$ . 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 $f(-x)$ . $\newline$ $f(-x)=-5(-x)^{4}-1-5(-x)^{6}$ $\newline$ Simplify the powers of $-x$ . $\newline$ $f(-x)=-5x^{4}-1-5x^{6}$
Compare $f(x)$ with $f(-x)$ : Compare $f(x)$ with $f(-x)$ . We have $f(x)=-5x^{4}-1-5x^{6}$ and $f(-x)=-5x^{4}-1-5x^{6}$ . Since $f(-x) = f(x)$ , the function $f(x)$ is an even function.

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