Assuming [x] means the closest integer to x
Answer:
[tex](-\infty, \infty)[/tex]
Step-by-step explanation:
We can see that for any integer [tex]x[/tex], there will always be a [tex][x][/tex], so there will always be a [tex][x]+1[/tex]. So, we don't need to worry about the domain impacting the range.
[tex][x][/tex] can be any integer from [tex]-\infty[/tex] to [tex]\infty[/tex], and as [tex]\infty+1=\infty[/tex](at least in terms of a function's range and domain), the range of [tex][x]+1[/tex] is equal to the range of [tex][x][/tex], which is [tex](-\infty, \infty)[/tex].
So, the answer is [tex]\boxed{(-\infty, \infty)}[/tex] and we're done!
