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Domain is where function will take valid values.

here f(x) =   x/(x + |x|)

Now see for which values this function can be of indeterminate form. For x = 0 it is 0 / 0 form so option A is ruled out. For negative values of x, x and |x| will cancel out each other and make the function infinity so option B and D also ruled out.

So option C is correct.
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