> continuous at exactly one place (0) and nowhere else after a bit of thought, less surprising if we regard g(x) as a function that is defined pointwise as eit

> continuous at exactly one place (0) and nowhere else after a bit of thought, less surprising if we regard g(x) as a function that is defined pointwise as either i(x) = x or z(x) = 0 depending on some highly discontinuous property of x z(x) = 0 is a pretty good approximation of i(x) = x at x=0