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Is this an even function?

  1. May 11, 2013 #1
    Is

    [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

    CompuChip

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    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

    HallsofIvy

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    If f is any function whatsoever, then f(|x|) is an even function.
     
  5. May 11, 2013 #4
    Thanks for the response.
     
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