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.

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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?