1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Odd/Even function query

  1. Oct 13, 2013 #1
    Hi all,

    Doing some odd/even functions questions and I've had a bit of a weird mind fart when trying to remember why we process the equations like we do.....It's probably real simple, but I just can't remember why we 'move' one of the signs to where it ends up....please bear with me (and don't laugh too much)....

    While determining if f(x) = (x^2 + 2)sin(x) = odd/even

    f(-x) = (-x^2 + 2)sin(-x)

    (-x^2 = x^2 and sin(-x) = -sin(x)

    therefore the next line should theoretically be

    f(-x) = (x^2 + 2)(-sin(x))

    but (after checking on wolfram and it's giving it as an odd function) I'm sure we need it to be =

    f(-x) = - (x^2 + 2)sin(x)

    thus making f(-x) = -f(x) and hence odd

    but for the life of me, I can't remember why we move the - sign infront of 'sin' to the beginning, making it - (x^2 + 2).
    Is it just for 'ease' or is there a specific reason? I can remember seeing it before, but like I said, I just can't remember 'why'.

    Any simple explanations out there would be appreciated...
  2. jcsd
  3. Oct 13, 2013 #2


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    Dearly Missed

    f(-x) = (x^2 + 2)(-sin(x))=(x^2 + 2)*((-1)*sin(x))=(-1)*((x^2 + 2)*sin(x))=-(x^2 + 2)*sin(x)
  4. Oct 13, 2013 #3


    User Avatar
    Science Advisor

    You are probably entering the function into Wolfram incorrectly. (-x)^2 is NOT the same as -x^2!

    If x= 4, (-x)^2= (-4)^2= 16 but -x^2= -(4^2)= -16.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook