The domain of the function $f(x)=\sqrt{x-1}+\sqrt{6-x}$ is

The domain of the function $f(x)=\sqrt{x-1}+\sqrt{6-x}$ is
  1. $[1, \infty)$
  2. $[1,6]$
  3. $(-\infty, 6]$
  4. $(-\infty, 6)$

Solution

$f(x)=\sqrt{x-1}+\sqrt{6-x}$ Here $\mathrm{f}(\mathrm{x})$ is defined when $x-1 \geq 0$ and $6-x \geq 0 \quad$ i.e. $x \geq 1$ and $x-6 \leq 0 \quad$ i.e. $x \geq 1$ and $x \leq 6$ $\therefore$ Domain of $\mathrm{f}(\mathrm{x})$ is $[1,6]$

Asked in: MHT CET 2021 (22 Sep Shift 1)

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