Question

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

Answer 1

The given function is neither odd nor even.

Explanation:

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.