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Determine whether the function
f(x)=x^(6)+7x^(2)-1 is even, odd or neither.
odd
neither
even

Determine whether the function $f(x)=x^{6}+7 x^{2}-1$ 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)=x^{6}+7 x^{2}-1

is even, odd or neither.

\newline

odd

\newline

neither

\newline

even

Determine Function Type: To determine if the function $f(x)$ is even, odd, or neither, we need to compare $f(x)$ with $f(-x)$ . If $f(-x) = f(x)$ , then the function is even. If $f(-x) = -f(x)$ , then the function is odd. If neither condition is met, the function is neither even nor odd.
Substitute $-x$ in Function: First, let's find $f(-x)$ by substituting $-x$ for $x$ in the function $f(x)=x^6+7x^2-1$ . $\newline$ $f(-x)=(-x)^6+7(-x)^2-1$
Simplify $f(-x)$ Expression: Now, simplify the expression for $f(-x)$ .
$f(-x)=(-x)^6+7(-x)^2-1$
$f(-x)=x^6+7x^2-1$
Compare $f(x)$ and $f(-x)$ : We have: $f(x)=x^6+7x^2-1$ $f(-x)=x^6+7x^2-1$ Since $f(-x) = f(x)$ , the function $f(x)$ is an even function.

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