# The domain of definition of the function f(x) =

Question:

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

(a) [1, ∞)

(b) (−∞, 3)

(c) (1, 3)

(d) [1, 3]

Solution:

(d) [1, 3]

$f(x)=\sqrt{x-1}+\sqrt{3-x}$

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

$(x-1) \geq 0$

$\Rightarrow x \geq 1 \quad \ldots(1)$

and $(3-x) \geq 0$

$\Rightarrow 3 \leq x \quad \ldots(2)$

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

$x \in[1,3]$