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Let 
f(x)=-6x^(3)-6x. Determine 
f(-x) first and then determine whether the function is even, odd, or neither. Write even if the function is even, odd if the function is odd, and neither if the function is neither even nor odd.

f(-x)=

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Even/Odd/Neither: 
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Let f(x)=6x36x f(x)=-6 x^{3}-6 x . Determine f(x) f(-x) first and then determine whether the function is even, odd, or neither. Write even if the function is even, odd if the function is odd, and neither if the function is neither even nor odd.\newlinef(x)= f(-x)= \newline \square \newlineEven/Odd/Neither: \square

Full solution

Q. Let f(x)=6x36x f(x)=-6 x^{3}-6 x . Determine f(x) f(-x) first and then determine whether the function is even, odd, or neither. Write even if the function is even, odd if the function is odd, and neither if the function is neither even nor odd.\newlinef(x)= f(-x)= \newline \square \newlineEven/Odd/Neither: \square
  1. Calculate f(x)f(-x): Calculate f(x)f(-x) by substituting x-x for xx in the function f(x)=6x36xf(x) = -6x^3 - 6x.\newlinef(x)=6(x)36(x)f(-x) = -6(-x)^3 - 6(-x)\newline =6(x3)+6x= -6(-x^3) + 6x\newline =6x3+6x= 6x^3 + 6x
  2. Determine function type: Determine if the function is even, odd, or neither. Compare f(x)f(x) and f(x)f(-x).
    f(x)=6x36xf(x) = -6x^3 - 6x
    f(x)=6x3+6xf(-x) = 6x^3 + 6x
    Since f(x)=f(x)f(-x) = -f(x), the function is odd.

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