Question

Domain of the function defined by f(x) = 1x - 1 + 13 – x is ......​

Answer 1

Given function is:

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

Since square root function is defined only for non negative numbers,

$\implies {x - 1} \geqslant 0$

$\implies \: x \geqslant 1 - - - (1.)$

Also

$\implies \: 3 - x \geqslant 0$

$\implies 3 \geqslant x - - - (2.)$

From the relations (1.) and (2.) we get

$\implies \: 1 \leqslant x \leqslant 3$

Or

$[1,3]$

Domain is the set of all possible values of x.

Hence the domain of the given function is [1,3].