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Is the function h(x)=−3x8+x4−2x2h(x) = -3x^8 + x^4 - 2x^2 even, odd, or neither?\newlineChoices:\newline(A)even\newline(B)odd\newline(C)neither

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Full solution

Q. Is the function h(x)=−3x8+x4−2x2h(x) = -3x^8 + x^4 - 2x^2 even, odd, or neither?\newlineChoices:\newline(A)even\newline(B)odd\newline(C)neither
  1. Calculate h(−x)h(-x): Calculate h(−x)h(-x) by substituting −x-x for xx in the function h(x)h(x).\newlineh(−x)=−3(−x)8+(−x)4−2(−x)2h(-x) = -3(-x)^8 + (-x)^4 - 2(-x)^2
  2. Simplify h(−x)h(-x): Simplify the function h(−x)h(-x).h(−x)=−3x8+x4−2x2h(-x) = -3x^8 + x^4 - 2x^2
  3. Compare h(x)h(x) and h(−x)h(-x): Compare h(x)h(x) and h(−x)h(-x).\newlineSince h(−x)=h(x)h(-x) = h(x), the function h(x)h(x) is even.

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