Question

Determine if the relation is even, odd, or neither.
f(x)=x sin x

Answer 1

What does it mean for it to be odd or even (as a function)
It all has to do with how f(-x) behaves.

If f(-x) = f(x), it's even.
if f(-x) = -f(x), it's odd.

Try out f(-x), what do you get?

Answer 2

Of course, if f(-x) is neither f(x) nor -f(x), then it's neither odd nor even.

Answer 3

that's the problem idk how to solve -xsin-x??

Answer 4

LOL You're on the right track :)
\[\Large f(-x) = (-x)\sin(-x)\]
Now, you can just note that sin itself is an odd function:
IE
\[\Large \sin(-x) = \color{blue}{-\sin(x)}\]

Answer 5

Can you take it from here?

Answer 6

yes I can thanks :)

Answer 7

Good. Your answer?

Answer 8

lol sorry, I just came to check up on stuff :)
I need to go now ^_^

Hopefully you got the concept straight:
f(-x) = f(x) ---> even function
f(-x) = -f(x) ---> odd function
otherwise, it's neither.

Get it? Got it? Good :)
Signing off
---------------------------------
Terence out