If f is injective (one-to-one) and continuous on an interval I, then the inverse function f^-1 exists and is continuous on a corresponding interval J (in the image or range of f). More precisely, if f : I -> J is one-to-one, and J is the image f(I) of I (in other words, J is the range of f), then f^-1 : J -> I exists and is continuous.