If $\displaystyle f(x)=\frac{1}{x-1}$ for $\displaystyle x>2$ and $\displaystyle f(x)=x+1$ for $\displaystyle 2 \geq x$, find $\displaystyle f(a-2)$ in terms of a.

Normally I would simply substitute a in, but I don't know if that is the right way to go about things?

I think I should have considered pre-calc a little more carefully before going into calc :)