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How do you determine if #f(x) = (x^3 - x)/(x^3 - 4x)# is an even or odd function?

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1 Answer

Jun 5, 2016

#f(x)# is even.

Explanation:

If a function is odd, then #f(-x)=-f(x)#. If a function is even, then #f(-x)=f(x)#. Plugging in #-x# into the given function gives

#f(-x)=((-x)^3-(-x))/((-x)^3-4(-x))=(-(x^3-x))/(-(x^3-4x))=f(x)#

Hence #f(x)# is even.

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