Continuous function/R/Intermediate value theorem/Fact

Let ${\displaystyle {}a\leq b}$ be real numbers, and let ${\displaystyle {}f\colon [a,b]\rightarrow \mathbb {R} }$ be a continuous function. Let ${\displaystyle {}u\in \mathbb {R} }$ be a real number between ${\displaystyle {}f(a)}$ and ${\displaystyle {}f(b)}$.

Then there exists an

${\displaystyle {}x\in [a,b]}$ such that

${\displaystyle {}f(x)=u}$.