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Is the function n(x)=−x4+3x2−4n(x) = -x^4 + 3x^2 - 4 even, odd, or neither?\newlineChoices:\newline(A)even\newline(B)odd\newline(C)neither

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Q. Is the function n(x)=−x4+3x2−4n(x) = -x^4 + 3x^2 - 4 even, odd, or neither?\newlineChoices:\newline(A)even\newline(B)odd\newline(C)neither
  1. Substitute −x-x for xx: n(x)=−x4+3x2−4n(x) = -x^4 + 3x^2 - 4\newlineFind n(−x)n(-x) by substituting −x-x for xx.\newlinen(−x)=−(−x)4+3(−x)2−4n(-x) = -(-x)^4 + 3(-x)^2 - 4
  2. Simplify the equation: n(−x)=−(−x)4+3(−x)2−4n(-x) = -(-x)^4 + 3(-x)^2 - 4\newlineSimplify the equation.\newlinen(−x)=−x4+3x2−4n(-x) = -x^4 + 3x^2 - 4
  3. Compare n(x)n(x) and n(−x)n(-x): Compare n(x)n(x) and n(−x)n(-x). We got n(x)=−x4+3x2−4n(x) = -x^4 + 3x^2 - 4 and n(−x)=−(−x)4+3(−x)2−4n(-x) = -(-x)^4 + 3(-x)^2 - 4. Since n(−x)=n(x)n(-x) = n(x), n(x)n(x) is an even function.

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