The domain of definition of f(x)

(a) (−∞, −3] ∪ (2, 5)

$f(x)=\sqrt{\frac{x+3}{(2-x)(x-5)}}$

For $\mathrm{f}(\mathrm{x})$ to be defined,

$(2-x)(x-5) \neq 0$

$\Rightarrow x \neq 2,5$    ....(1)

Also, $\frac{(x+3)}{(2-x)(x-5)} \geq 0$

$\Rightarrow \frac{(x+3)(2-x)(x-5)}{(2-x)^{2}(x-5)^{2}} \geq 0$

$\Rightarrow(x+3)(x-2)(x-5) \leq 0$

$\Rightarrow x \in(-\infty,-3] \cup(2,5) \quad \ldots(2)$

From $(1)$ and $(2)$

$x \in(-\infty,-3] \cup(2,5)$