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Math Help - Even, odd or neither function

  1. #1
    Newbie
    Joined
    Sep 2009
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    7

    Even, odd or neither function

    The question states:

    Suppose g is a function defined for all x > 0 which satisfies the following properties for all a, b > 0:

    g(1) = 0

    g(a/b) = g(a) - g(b)

    Determine whether the function f(x) = g(x+ root(x^2+1)) is even, odd or neither, and justify your answer.

    -----------------------------------------------------------------------

    Well I was thinking that g could be a logarithmic function, and x+ root(x^2+1) is neither even nor odd, so f(x) is a neither function...

    I think I'm approaching this the wrong way... Can anyone help me out please?
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  2. #2
    Senior Member
    Joined
    Jul 2009
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    397
    Hi skeeterrr

    I'm not sure how to approach it but I think drawing the graph will be helpful
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  3. #3
    Member
    Joined
    Apr 2008
    Posts
    191
    I think the best way would be to solve f(x) + f(-x) & f(x) - f(-x) to see whether f is odd or even.
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