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The set of points where f(x) = x/(1 + |x|) is differentiable is

1. (-∞, 0) ∪ (0, ∞)
2. (-∞, -1) ∪ (-1, ∞)
3. (-∞, ∞)
4. (0, ∞)

Correct answer: (-∞, ∞)

Solution

For x>0, f=x/(1+x) with f'=1/(1+x)^2; for x<0, f=x/(1-x) with f'=1/(1-x)^2. Both one-sided derivatives at 0 equal 1 and f is continuous, so f is differentiable everywhere -> domain (-inf, inf).

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