My textbook always says things like "[...] such that f is invertible, continuous, and f^-1 is continuous also" and " [...] such that g is invertible, smooth, and g^-1 is smooth also"(adsbygoogle = window.adsbygoogle || []).push({});

But doesn't it follow from "f is conitnuous" that "f^-1 is continuous", and same thing for smooth?

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