Question

The domain of definition of the function $f\left(x\right)=\sqrt{x-1}+\sqrt{3-x}$ is

(a) [1, ∞)
(b) (−∞, 3)
(c) (1, 3)
(d) [1, 3]

Answer 1

(d) [1, 3]

$f\left(x\right)=\sqrt{x-1}+\sqrt{3-x}$
$$\begin{gathered} \mathrm{For}\mathrm{f}\left(\mathrm{x}\right)\mathrm{to}\mathrm{be}\mathrm{defined}, \\ \left(x-1\right)\ge 0 \\ \Rightarrow x\ge 1...\left(1\right) \\ \mathrm{and}\left(3-x\right)\ge 0 \\ \Rightarrow 3\le x...\left(2\right) \\ \mathrm{From}\left(1\right)\mathrm{and}\left(2\right), \\ x\in [1,3] \end{gathered}$$