2. Given two functions f and g, we say that g is a quasi-inverse of f when "There exists a non-empty, open interval I contained in the domain of f, such that the restriction of f to I is one-to-one, and g is the inverse of that restriction." For example, arctan is a quasi-inverse of tan. Construct a function f that satisfies all the following properties at once: (a) The domain of f is R. (b) f is differentiable. (c) For every c > 0 there exists a quasi-inverse g off such that g is differentiable at 0 and and 0

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