Intermediate value theorem

In mathematical analysis, the intermediate value theorem states that if f {\displaystyle f} is a continuous function whose domain contains the interval [a, b] and s {\displaystyle s} is a number such that f ( a ) < s < f ( b ) {\displaystyle f(a)<s<f(b)} , then there exists some x {\displaystyle x} between a {\displaystyle a} and b {\displaystyle b} such that f ( x ) = s {\displaystyle f(x)=s} . That is, the image of a continuous function over an interval is itself an interval that contains f ( a ) , f ( b ) {\displaystyle f(a),f(b)} .

Source: Wikipedia — Intermediate value theorem (CC BY-SA 4.0)