# What type of function satisfy a type of growth condition?

• A
Vulture1991
Let ##f:\mathbb{R}^n\rightarrow\mathbb{R}^n##. Is there any class of function and some type of "growth conditions" such that bounds like below can be established:

||f(x)||\geq g\left( \text{dist}(x,\mathcal{X})\right),

with ##\mathcal{X}:= \{x:f(x)=0\}## (zero set) and some function ##g## (like a homogeneous function).

I am interested to know the class of functions. Any help will help a lot. Thanks in advance