1.
Let the sets AA and BB denote the domain and range respectively of the function
f(x)=x−1[x]−1f(x)=\frac{\sqrt{x-1}}{[x]-1}
where [x][x] denotes the smallest integer greater than or equal to xx. Then among the statements:
(S1) A∩B=(1,∞)−N(S_1)\ A\cap B=(1,\infty)-\mathbb N
(S2) A∪B=(1,∞)(S_2)\ A\cup B=(1,\infty)
Sets, Relations and Functions - Hard - Question