Question

Find the domain of definition of the following function.
$y=\sqrt{\frac{x^2-7x+12}{x^2-6x-3}}.$

Answer 1

For $x^2-6x-3=0$

$x=\frac{6\pm \sqrt{36+12}}{2}=\frac{6\pm \sqrt{48}}{2}=3\pm \sqrt{12}$

so, $f\left(x\right)=\sqrt{\frac{(x-4)(x-3)}{(x-3+\sqrt{12})(x-3-\sqrt{12})}}$

s0,domain of $f\left(x\right)=(-\infty ,-3-\sqrt{12})\cup (-3+\sqrt{12},3)\cup (4,\infty )$