The fundamental group of a topological space is isomorphic with its connected component fundamental group

Question

can you help me with this problem of fundamental groups? suppose that $X$ is a topological space, let's fix a point on $X$ like $p\in{X}$. Thus I want to prove that the fundamental group of $X$ at $p$ is isomorphic to the fundamental group of connected component of $X$ at $p$. Should I build a bijection between them and prove its existence? or should I use theorems of the fundamental theorems and covering spaces... to prove this proposition? I really need help to solve this problem, thank you all!