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Is the function d(x)=x4−x2d(x) = x^4 - x^2 even, odd, or neither?\newlineChoices:\newline(A)even\newline(B)odd\newline(C)neither

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Q. Is the function d(x)=x4−x2d(x) = x^4 - x^2 even, odd, or neither?\newlineChoices:\newline(A)even\newline(B)odd\newline(C)neither
  1. Substitute and Simplify: d(x)=x4−x2d(x) = x^4 - x^2\newlineLet's find d(−x)d(-x) by substituting −x-x for xx.\newlined(−x)=(−x)4−(−x)2d(-x) = (-x)^4 - (-x)^2
  2. Compare Functions: d(−x)=(−x)4−(−x)2d(-x) = (-x)^4 - (-x)^2\newlineSimplify the right side.\newlined(−x)=x4−x2d(-x) = x^4 - x^2
  3. Identify Even Function: Compare d(x)d(x) and d(−x)d(-x). We have d(x)=x4−x2d(x) = x^4 - x^2 and d(−x)=x4−x2d(-x) = x^4 - x^2. Since d(−x)=d(x)d(-x) = d(x), d(x)d(x) is an even function.

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