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Is the function v(x)=−x7+8x5v(x) = -x^7 + 8x^5 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)=−x7+8x5v(x) = -x^7 + 8x^5 even, odd, or neither?\newlineChoices:\newline(A)even\newline(B)odd\newline(C)neither
  1. Select function for v(−x)v(-x): v(x)=−x7+8x5v(x) = -x^7 + 8x^5\newlineSelect the function for v(−x)v(-x).\newlineSubstitute −x-x for xx in v(x)=−x7+8x5v(x) = -x^7 + 8x^5.\newlinev(−x)=−(−x)7+8(−x)5v(-x) = -(-x)^7 + 8(-x)^5
  2. Simplify right side: v(−x)=−(−x)7+8(−x)5v(-x) = -(-x)^7 + 8(-x)^5\newlineSimplify the right side of the function.\newlinev(−x)=−(−1)7×x7+8(−1)5×x5v(-x) = -(-1)^7 \times x^7 + 8(-1)^5 \times x^5\newlinev(−x)=x7−8x5v(-x) = x^7 - 8x^5
  3. Determine function type: We have:\newlinev(x)=−x7+8x5v(x) = -x^7 + 8x^5\newlinev(−x)=x7−8x5v(-x) = x^7 - 8x^5\newlineIs the function v(x)v(x) even, odd, or neither?\newlineSince v(−x)=−v(x)v(-x) = -v(x), v(x)v(x) is an odd function.

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