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Is the function m(x)=−4x5+6xm(x) = -4x^5 + 6x even, odd, or neither?\newlineChoices:\newline(A)even\newline(B)odd\newline(C)neither

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Full solution

Q. Is the function m(x)=−4x5+6xm(x) = -4x^5 + 6x even, odd, or neither?\newlineChoices:\newline(A)even\newline(B)odd\newline(C)neither
  1. Check Even by Evaluating: Check if m(x)m(x) is even by evaluating m(−x)m(-x) and comparing it to m(x)m(x).m(−x)=−4(−x)5+6(−x)m(-x) = -4(-x)^5 + 6(-x)
  2. Simplify m(−x)m(-x): Simplify m(−x)m(-x).
    m(−x)=−4(−x)5−6xm(-x) = -4(-x)^5 - 6x
    m(−x)=4x5−6xm(-x) = 4x^5 - 6x
  3. Compare m(−x)m(-x) with m(x)m(x): Compare m(−x)m(-x) with m(x)m(x).
    m(x)=−4x5+6xm(x) = -4x^5 + 6x
    m(−x)=4x5−6xm(-x) = 4x^5 - 6x
    Since m(−x)m(-x) is not equal to m(x)m(x), m(x)m(x) is not even.
  4. Check Odd by Evaluating: Check if m(x)m(x) is odd by evaluating if m(−x)m(-x) is equal to −m(x)-m(x).
    −m(x)=−(−4x5+6x)-m(x) = -(-4x^5 + 6x)
    −m(x)=4x5−6x-m(x) = 4x^5 - 6x
  5. Compare −m(x)-m(x) with m(−x)m(-x): Compare −m(x)-m(x) with m(−x)m(-x).
    −m(x)=4x5−6x-m(x) = 4x^5 - 6x
    m(−x)=4x5−6xm(-x) = 4x^5 - 6x
    Since m(−x)m(-x) is equal to −m(x)-m(x), m(x)m(x) is odd.

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