Is the following function continuous on $X$?

Is the following function continuous on $X$?

Justify: Let a metric space $(X,d)$ and for $k\in\Lambda, f_k:X\to\mathbb
R$ be continuous where $f_k\ge0~\forall~k\in\Lambda$. Then
$$f:x\mapsto\displaystyle\inf_{k\in\Lambda}f_k(x)$$ is continuous.