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Is the function g(x)=2x8−x6+7g(x) = 2x^8 - x^6 + 7 even, odd, or neither?\newlineChoices:\newline(A)even\newline(B)odd\newline(C)neither

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Q. Is the function g(x)=2x8−x6+7g(x) = 2x^8 - x^6 + 7 even, odd, or neither?\newlineChoices:\newline(A)even\newline(B)odd\newline(C)neither
  1. Define g(x)g(x): g(x)=2x8−x6+7g(x) = 2x^8 - x^6 + 7\newlineSelect the function for g(−x)g(-x).\newlineSubstitute −x-x for xx in g(x)=2x8−x6+7g(x) = 2x^8 - x^6 + 7.\newlineg(−x)=2(−x)8−(−x)6+7g(-x) = 2(-x)^8 - (-x)^6 + 7
  2. Substitute −x-x: g(−x)=2(−x)8−(−x)6+7g(-x) = 2(-x)^8 - (-x)^6 + 7\newlineSimplify the right side of the function.\newlineg(−x)=2x8−x6+7g(-x) = 2x^8 - x^6 + 7
  3. Simplify g(−x)g(-x): We have: \newlineg(x)=2x8−x6+7g(x) = 2x^8 - x^6 + 7 \newlineg(−x)=2(−x)8−(−x)6+7g(-x) = 2(-x)^8 - (-x)^6 + 7 \newlineIs the function g(x)g(x) even, odd, or neither?\newlineSince g(−x)=g(x)g(-x) = g(x), g(x)g(x) is an even function.

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