How do you determine if #f(x)= 1/(x³-3x)# is an even or odd function?

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Answer 1 · 2018-05-07T18:54:27

Odd function.

Recall that, #f(-x)=-f(x), AA x in D_f iff f" is odd"#.

In our case, #f(x)=1/(x^3-3x)#.

#:. f(-x)=1/{(-x)^3-3(-x)}#,

#=1/{-x^3+3x}#,

#=-{1/(x^3-3x)}#,

# rArr f(-x)=-f(x)#.

Therefore, #f# is odd.