# Converse Of Intermediate Value Theorem

**Calculus**Level pending

A function \(f: [a,b] \to \mathbb{R}\) (where \(a\), \(b\) might equal \(\pm \infty\)) is said to have the *intermediate value property* if for every \[x \in [\min(f(a), f(b)), \max(f(a), f(b))],\] there exists some \(c\in [a,b]\) such that \(f(c) = x\).

The intermediate value theorem states that if \(f\) is continuous, then \(f\) has the intermediate value property. Is the converse of this theorem true? That is, if a function has the intermediate value property, must it be continuous on its domain?

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