How do you know if #f(x)=x^4+3x^-4+2x^-1# is an even or odd function?

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Answer 1 · 2016-04-17T08:46:25

#f(x)# is neither even nor odd.

A function #f(x)# is even if #f(-x)=f(x)#

and is odd if #f(-x)=-f(x)#

As #f(x)=x^4+3x^(-4)+2x^(-1)#

#f(-x)=(-x)^4+3(-x)^(-4)+2(-x)^(-1)#

= #x^4+3x^(-4)-2x^(-1)# (as #x^(-1)# is an odd power)

Hence #f(-x)!=f(x)# as also #f(-x)!=-f(x)#

Hence, #f(x)# is neither even nor odd.