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Is the function v(x)=x5−4x4v(x) = x^5 - 4x^4 even, odd, or neither?\newlineChoices:\newline(A)even\newline(B)odd\newline(C)neither

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Full solution

Q. Is the function v(x)=x5−4x4v(x) = x^5 - 4x^4 even, odd, or neither?\newlineChoices:\newline(A)even\newline(B)odd\newline(C)neither
  1. Substitute and Simplify: v(x)=x5−4x4v(x) = x^5 - 4x^4\newlineLet's find v(−x)v(-x) by substituting −x-x for xx.\newlinev(−x)=(−x)5−4(−x)4v(-x) = (-x)^5 - 4(-x)^4
  2. Comparison of v(x)v(x) and v(−x)v(-x): v(−x)=(−x)5−4(−x)4v(-x) = (-x)^5 - 4(-x)^4\newlineSimplify the right side of the equation.\newlinev(−x)=−x5−4x4v(-x) = -x^5 - 4x^4
  3. Comparison of v(x)v(x) and v(−x)v(-x): v(−x)=(−x)5−4(−x)4v(-x) = (-x)^5 - 4(-x)^4 Simplify the right side of the equation. v(−x)=−x5−4x4v(-x) = -x^5 - 4x^4 Compare v(x)v(x) and v(−x)v(-x). We have v(x)=x5−4x4v(x) = x^5 - 4x^4 and v(−x)=−x5−4x4v(-x) = -x^5 - 4x^4. Since v(−x)v(-x) is not equal to v(x)v(x) and not equal to v(−x)v(-x)00, v(x)v(x) is neither even nor odd.

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