Answer
$(-\infty,\infty)$
Work Step by Step
$r(t) = \frac{1}{(t-1)} \textbf i + 3t \textbf j\\
r'(t) = -\frac{1}{(t-1)^2} \textbf i +3 \textbf j $
So, we do not get $r'(t) = 0 \textbf i +0 \textbf j $ for any value of $t$. The curve is smooth on the interval $(-\infty,\infty)$.
