Find the range of the function
\[p(x) = \frac{x^2 + x + 1}{x^2 + 1}.\]
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Find the range of the function
\[p(x) = \frac{x^2 + x + 1}{x^2 + 1}.\]
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
\left[ \frac{1}{2}, \frac{3}{2} \right]
Find the range of the function
\[p(x) = \frac{x^2 + x + 1}{x^2 + 1}.\]
train