Answer
$D_f=(-\infty,\infty)$; $R_f=(-\infty,\infty)$
$D_g=[0,\infty)$; $R_g=[0,\infty)$
Work Step by Step
We are given the functions:
$f(x)=x^{1/7}$
$g(x)=x^{1/4}$
Rewrite the functions:
$f(x)=\sqrt[7] x$
$g(x)=\sqrt[4] x$
As the order of the radical in $f(x)$ is odd, therefore its domain and range are:
$D_f=(-\infty,\infty)$
$R_f=(-\infty,\infty)$
As the order of the radical in $g(x)$ is even, therefore its domain and range are:
$D_g=[0,\infty)$
$R_g=[0,\infty)$
