How can we define 'coincides' in this context?

Question

Consider the below question

Let $f : D \rightarrow \mathbb{R}$, and assume that $f$ coincides with some differentiable function $g : \mathbb{R} \rightarrow \mathbb{R}$ for all $x \in (b, c) \subset D$. Prove that $f$ is differentiable at $a$ for all $a \in (b, c)$.

I am not interested in how to answer this question. I wish to understand exactly what is meant by the term coincides in this context.

Does it mean that $f(x) = g(x)$ for all $x$ in some interval?

Answer 1

Yes. It means $f(x)=g(x)$ for $x\in(b,c)$.