Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Is this an even function?

  1. May 11, 2013 #1

    [tex]f(x)=\sin[a(b+|x|)]\;\hbox{ and }\; g(x)=\sin[a(b-|x|)][/tex]

    Both EVEN function?

    It looks even function to me even though it's a sine function( odd function), but the |x| make it an even function where f(-x)=f(x).
    Last edited: May 11, 2013
  2. jcsd
  3. May 11, 2013 #2


    User Avatar
    Science Advisor
    Homework Helper

    Yes, f(-x) = f(x) is the definition of an even function, and as you noted it satisfies that definition. To verify you can plot it and note that it is symmetric around the y-axis.
  4. May 11, 2013 #3


    User Avatar
    Science Advisor

    If f is any function whatsoever, then f(|x|) is an even function.
  5. May 11, 2013 #4
    Thanks for the response.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook