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

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

• A. (−∞, ∞)
• B. (−∞, 0) ∪ (0, ∞)
• C. (0, ∞)
• D. (−∞, 0)

Answer: A) (−∞, ∞)

Explanation: f(x) = x/(1+x) for x≥0, and x/(1−x) for x<0. Check at x=0: f(0)=0. LHD = lim(h→0) [−h/(1+h) − 0]/(−h) = 1/(1+h) →1. RHD = lim [h/(1+h)]/h = 1/(1+h) →1. So differentiable everywhere.