$\text{a)}f\left(x\right)=\frac{1}{x-1}$  

$\text{b)}f\left(x\right)=\frac{1}{\left(x+3\right)\left(x-6\right)}$  

$\text{c)}f\left(x\right)=\frac{1}{\left(x+4\right)x\left(x-5\right)}$  

$\text{d)}f\left(x\right)=\frac{1}{\sqrt{-x}}$  

$\text{e)}f\left(x\right)=\sqrt{x-4}$  

$\text{f)}f\left(x\right)=\frac{1}{\sqrt{x-5}}$