The domain of the definition of the function.

$\text{'}f\text{'}$ is defined if $\frac{x-2}{x+3}>0$ and $\frac{x-2}{x+3}\ne 1$

which true if $x\in (2,\infty )$ or $x\in (-\infty ,-3)$

Hence the domain of the function in (i) is $R~[-3,2]$

The function (ii) is defined if $x\ge -2,1-x>0$ and $1-x\ne 0$ and $x\in [-1,1]$

Hence domain in this case $[-1,1)-\left\{0\right\} x-\left\{x\right\}=0$

If and only $x\in I$