Is the converse of the second part of Theorem 5.7 true? That is, if a function is
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Is the converse of the second part of Theorem 5.7 true? That is, if a function is one-to-one (and therefore has an inverse function), then must the function be strictly monotonic? If so, prove it. If not, give a counterexample.
Data from in Theorem 5.7
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THEOREM 5.7 The Existence of an Inverse Function 1. A function has an inverse function if and only if it is one-to-one. 2. If f is strictly monotonic on its entire domain, then it is one-to-one and therefore has an inverse function.
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