Answer
$div G=f(x,y,z)$
It has been proved that every continuous function $f$ is the divergence of some vector field.
Work Step by Step
Let us consider that the vector field $G=\lt g(x,y,z) ,0,0 \gt$
where, $g(x,y,z) =\int_0^x f(t,y,z) dx$
$div F=\dfrac{\partial A}{\partial x}+\dfrac{\partial B}{\partial y}+\dfrac{\partial C}{\partial z}$
Then,we have
$div F=\dfrac{\partial }{\partial x}[\int_0^x f(t,y,z) dx]+\dfrac{\partial (0)}{\partial y}+\dfrac{\partial (0)}{\partial z}$
Thus, $div G=f(x,y,z) +0+0=f(x,y,z)$
Hence it has been proved that every continuous function $f$ is the divergence of some vector field.
