Question

Find the domains of definition of the following functions.
$y=\frac{x}{\sqrt{x^2-5x+6}}.$

Answer 1

R.E.F image

Find domains of functions

$y=\frac{x}{\sqrt{x^2-5x+6}}$ for $\frac{1}{\sqrt{y\left(x\right)}},y\left(x\right)>0$

$x^2-5x+6>0$

$(x-2)(x-3)>0$

$xϵ(-\infty ,2){\cup }_1(3,\infty )$

domain of function

$xϵ(-\infty ,2)\cup (3,\infty )$