Given continuous function $g:[a,b{]}^{n}\subset {\mathbb{R}}^{n}\to \mathbb{R}$. By Weistress $g$ has a max and a min.

Can I also conclude its image contains all values in-between this maximum and minimum?

I need this result to complete a proof but cannot seem to find a generalisation of the Intermediate Value Theorem to ${\mathbb{R}}^{n}$.

Can I also conclude its image contains all values in-between this maximum and minimum?

I need this result to complete a proof but cannot seem to find a generalisation of the Intermediate Value Theorem to ${\mathbb{R}}^{n}$.