Question

Find the domain of $f\left(x\right)=\sqrt{\left(\left[x\right]-1\right)}+\sqrt{\left(4-\left[x\right]\right)}$
(where[] represents the greater integer function)

Answer 1

$f\left(x\right)=\sqrt{\left[x\right]-1}+\sqrt{4-\left[x\right]}\left[x\right]-1\ge 0\left[x\right]\ge 1xϵ[1,\infty )-\left(i\right)4-\left[x\right]\ge 0\left[x\right]\le 4x<5-\left(ii\right)from\left(i\right)\&\left(ii\right)xϵ[1,5)$