How do you determine if # (x-1)^3(x-5)# is an even or odd function?

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Answer 1 · 2016-03-25T08:24:26

The given function is neither odd nor even.

If #f(-x)=f(x)# then the function is even,

but if #f(-x)=-f(x)# then the function is odd.

As #f(x)=(x-1)^3(x-5)#

#f(-x)=(-x-1)^3(-x-5)=(-(x+1))^3(-(x+5))# or

#f(-x)=(-(x+1)^3)(-(x+5))=(x+1)^3(x+5)#

Hence neither #f(-x)=f(x)# nor #f(-x)=-f(x)#

Hence the given function is neither odd nor even.