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Determine whether the function
f(x)=8x^(4)+x^(2)+x^(6) is even, odd or neither.
odd
even
neither

Determine whether the function $f(x)=8 x^{4}+x^{2}+x^{6}$ 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)=8 x^{4}+x^{2}+x^{6}

is even, odd or neither.

\newline

odd

\newline

even

\newline

neither

Select function for $f(-x)$ : $f(x)=8x^{4}+x^{2}+x^{6}$ $\newline$ Select the function for $f(-x)$ . $\newline$ Substitute $-x$ for $x$ in $f(x)=8x^{4}+x^{2}+x^{6}$ . $\newline$ $f(-x)=8(-x)^{4}+(-x)^{2}+(-x)^{6}$
Substitute $-x$ in $f(x)$ : $f(-x)=8(-x)^{4}+(-x)^{2}+(-x)^{6}$ $\newline$ Simplify the right side of the function. $\newline$ $f(-x)=8x^{4}+x^{2}+x^{6}$
Simplify right side: We have: $\newline$ $f(x)=8x^{4}+x^{2}+x^{6}$ $\newline$ $f(-x)=8x^{4}+x^{2}+x^{6}$ $\newline$ Is the function $f(x)$ even, odd, or neither? $\newline$ We have $f(x)=8x^{4}+x^{2}+x^{6}$ and $f(-x)=8x^{4}+x^{2}+x^{6}$ . $\newline$ Since $f(-x) = f(x)$ , $f(x)$ is an even function.

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