Question

Find the domain of the function $f\left(x\right)=\sqrt{x^2-5x+6}$.

Answer 1

Given, the function,

$f\left(x\right)=\sqrt{x^2-5x+6}$

or, $f\left(x\right)=\sqrt{(x-3)(x-2)}$.

The function will be defined if $(x-3)(x-2)\ge 0$

or, $x\ge 3$ or, $x\le 2$.

So $x\in (-\infty ,2]\cup [3,\infty )$.