The domain and range of \( f(x)=\frac{\sqrt{x^{2}}+3 x+2}{x-1} \) are-

A Dom \( -f=(-\infty, 1) \cup[2, \infty] \) , Range \( -f= \) \( (0, \infty) \)

B Dom \( -\mathrm{f}=(-\infty, 1] \cup[2, \infty] \) , Range \( -\mathrm{f}= \) \( [0, \infty) \)

C Dom \( -\mathrm{f}=(-\infty, 0] \cup[2, \infty) \) , Range \( -\mathrm{f}= \) \( [1, \infty) \)