G is a topological group acts on topological space $X$, is $f_{g}:X\rightarrow X, x\rightarrow g*x$ continuous?

Question

Let $G$ be a topological group acts on the topological space $X$, for an elememt $g\in G$, let's define the map $f:X\rightarrow X, f(x)=g*x$.

I am trying to find if $f$ is continuous?

my best thanks