Answer
Domain of $f(x)=\left(-\frac{2}{5}, \infty\right)$
Work Step by Step
$f(x)=\ln (5 x+2)$
For the function to be
defined, the expression within the log should be greater than $0$.
Thus,
$5 x+2>0$
$\Rightarrow 5 x>-2$
$\Rightarrow x>-\frac{2}{5}$
$\therefore$ Domain of $f(x)=\left(-\frac{2}{5}, \infty\right)$
