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

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Answer 1 · 2016-06-17T15:59:46

#y = (x^4+1)/(x^3-2x)# is an odd function.

An even function is one for which #f(-x) = f(x)# for all #x# in its domain.

An odd function is one for which #f(-x) = -f(x)# for all #x# in its domain.

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

Then:

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

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

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

#=-f(x)#

So #y = (x^4+1)/(x^3-2x)# is an odd function.

Answer 2 · 2016-06-17T16:09:12

Odd

You can calculate f(-x) and see if :

1)f(-x)=f(x), in this case y is even
2)f(-x)=-f(x), in this one it is odd

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

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

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

Therefore f(-x)=-f(x) and y is odd