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Determine algebraically whether each function has even symmetry, odd symmetry or neither use $f(x)=2x^4-6x^2+1$

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Even and odd functions

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Q. Determine algebraically whether each function has even symmetry, odd symmetry or neither use

f(x)=2x^4-6x^2+1

Define function $f(x)$ : Define the function $f(x)$ . The given function is $f(x) = 2x^4 - 6x^2 + 1$ . To determine if the function is even, odd, or neither, we will evaluate $f(-x)$ and compare it to $f(x)$ .
Calculate $f(-x)$ : Calculate $f(-x)$ . $\newline$ Substitute $-x$ for $x$ in $f(x)=2x^4−6x^2+1$ . $\newline$ $f(-x)=2(-x)^4−6(-x)^2+1$
Simplify $f(-x)$ : Simplify $f(-x)$ . $\newline$ Simplify the expression by calculating the powers of $-x$ . $\newline$ $f(-x)=2((-x)^4)−6((-x)^2)+1$ $\newline$ $f(-x)=2(x^4)−6(x^2)+1$ (since $(-x)^4=x^4$ and $(-x)^2=x^2$ )
Compare $f(-x)$ with $f(x)$ : Compare $f(-x)$ with $f(x)$ . We have $f(x)=2x^4-6x^2+1$ and $f(-x)=2x^4-6x^2+1$ . Since $f(-x) = f(x)$ , the function $f(x)$ is an even function.

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