The continuous random variable $T$ has probability density function given by
$$f_T(t)= \begin{cases} 0 & t <2, \\ \frac{2}{(t-1)^3} & t \ge 2. \end{cases}$$
Find the probability density function of $Y$, where $Y = \frac{1}{T-1}$.
I understand that I need to look at cumulative probability functions, but the answer seems not to be normalised, as I think my problem lies with dealing with the constraints on $t$.