Compute the domain of the function

$f(x)=\frac{1}{\lfloor x^2+3x+3\rfloor}$
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Compute the domain of the function

$f(x)=\frac{1}{\lfloor x^2+3x+3\rfloor}$
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
(-\infty,-2] \cup [-1,\infty)
Compute the domain of the function

$f(x)=\frac{1}{\lfloor x^2+3x+3\rfloor}$
train