Question

Find the domain of the following function:

$f\left(x\right)=\sqrt{x^2-5x+6}$, the domain is $(-\infty ,a)\cup [b,\infty )$, then a+b =

Answer 1

For real values of f(x),
$x^2-5x+6>0$
Or
$(x-2)(x-3)\ge 0$
$x\ge 3$ or $x\le 2$
Hence
$xϵ(-\infty ,2]\cup [3,\infty )$
Therefore
$a=3$ and $b=2$
Therefore
$a+b=3+2$
$=5$