Continuous real function/Positive/Positive in neighborhood/Exercise

Let ${}T\subseteq \mathbb {R}$ be a subset and let

$f\colon T\longrightarrow \mathbb {R}$

be a continuous function. Let ${}x\in T$ be a point such that ${}f(x)>0$. Prove that ${}f(y)>0$

for all ${}y$ in a non-empty open interval ${}]x-a,x+a[$.

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