Question

Find the domain of definition of the following function.
$y,=\sqrt{x-1}\sqrt{6-x}.$

Answer 1

$y=\sqrt{x-1}\sqrt{6-x}$

$y=\sqrt{(x-1)(6-x)}$

Product of $(x-1)$ and $(6-x)$ should be greater than or equal to zero.

$(x-1)(6-x)\ge 0$

$x\ge 1$

$(6-x)\ge 0$

$-x\ge -6$

$x\le 6$

So,domain of $y=[1,6]$

Domain $=1\le x\le 6$