Lipschitz and Locally Lipschitz

["Jason Pawloski"]

Let f:(0,1] -> R be defined as f(x) = 1/x, and g:[-1,1] -> R be defined
as g(x) = (x)^(1/3). Am I right in saying neither of these functions is
Lipschitz, f(x) is locally Lipschitz, and g(x) is not even locally
Lipschitz?