Question

Determine domain of the function $y=\frac{\sqrt{x-1}}{x^2-4},x\ge 1,x\ne -2,2$
if domain is$D=[1,\infty ]-k$, what is k?

Answer 1

$y=\frac{\sqrt{x-1}}{x^2-4}$
$x^2-4\ne 0$
$x^2\ne 4$
$x\ne 2,-2$...(i)
For real values of x
$x-1\ge 0$
$x\ge 1$ ...(ii)
Hence from i and ii
$xϵ[1,\infty )-\left\{2\right\}$
Hence $k=2$