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Is the function g(x)=2x7−x5−6x3g(x) = 2x^7 - x^5 - 6x^3 even, odd, or neither?\newlineChoices:\newline(A)even\newline(B)odd\newline(C)neither

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Q. Is the function g(x)=2x7−x5−6x3g(x) = 2x^7 - x^5 - 6x^3 even, odd, or neither?\newlineChoices:\newline(A)even\newline(B)odd\newline(C)neither
  1. Substitute in g(−x)g(-x): g(x)=2x7−x5−6x3g(x) = 2x^7 - x^5 - 6x^3\newlineFind g(−x)g(-x) by substituting −x-x for xx in g(x)g(x).\newlineg(−x)=2(−x)7−(−x)5−6(−x)3g(-x) = 2(-x)^7 - (-x)^5 - 6(-x)^3
  2. Simplify g(−x)g(-x): g(−x)=2(−x)7−(−x)5−6(−x)3g(-x) = 2(-x)^7 - (-x)^5 - 6(-x)^3\newlineSimplify the right side of the function.\newlineg(−x)=−2x7+x5+6x3g(-x) = -2x^7 + x^5 + 6x^3
  3. Compare g(x)g(x) and g(−x)g(-x): Compare g(x)g(x) and g(−x)g(-x). We have g(x)=2x7−x5−6x3g(x) = 2x^7 - x^5 - 6x^3 and g(−x)=−2x7+x5+6x3g(-x) = -2x^7 + x^5 + 6x^3. Since g(−x)=−g(x)g(-x) = -g(x), g(x)g(x) is an odd function.

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