Determine if the function f(x)=2x|x^3| is even, odd, or neither.

Question

hartnn · Answer

a function is even when f(x) = f(-x)
odd when f(x) = -f(-x)
to get f(-x) just replace x in f(x) by -x !

hartnn · Answer

what you for as f(-x) for your f(x) ?
could u find  it ?

hero · Answer

Just replace x with -x. If you get the same expression afterwards, then the function is even. If not, then it is not even.

anonymous · Answer

Thanks! :D

hero · Answer

@Anacia23, you fully understand what to do here?

anonymous · Answer

@Hero Yeah. Just couldn't find my math notes..

hero · Answer

I see. Well, as long as you know what to do. So what did you conclude? Is the function even, odd, or neither?

anonymous · Answer

I got an odd function.

zarkon · Answer

$$f(-x)=f(x)=2(-x)|(-x)^3|$$

$$=-2x|-(x)^3|$$

$$=-2x|x^3|=-f(x)$$

zarkon · Answer

ignore the f(x) in the first line

zarkon · Answer

$$f(-x)=2(-x)|(-x)^3|$$

hartnn · Answer

yeah, f(x) is indeed odd function :)

anonymous · Answer

Thanks so much guys! And thanks @hartnn I thought so too!

hartnn · Answer

welcome ^_^