Question

Find the domain of definition of the following function.
$y,=\sqrt{x^2-5x+6}.$

Answer 1

$y=\sqrt{x^2-5x+6}$

$y=\sqrt{x^2-3x-2x+6}$

$y=\sqrt{x(x+3)-2(x-3)}$

$y=\sqrt{(x-3)(x-2)}$

$(x-3)(x-2)\ge 0$

$x\ge 3$

$x\ge 2$

So, $x\ge 3$

the domain of $y=[3,\infty )$