$\sin^{-1}(\frac{1+x^2}{2x})$ is

continuous but not differentiable at x = 1 differentiable at x = 1 neither continuous nor differentiable at x = 1 continuous everywhere

neither continuous nor differentiable at x = 1

$\sin^{-1}(\frac{1+x^2}{2x})$ is defined only for x = – 1 and x = 1. Hence (C) is the correct answer.