Let \[f(x)={{x}^{2}}+3x-3,x>0.\] If n points \[{{x}_{1}},{{x}_{2}},{{x}_{3}},...{{x}_{n}}\] are so chosen on the x-axis such that (i) \[\frac{1}{n}\sum\limits_{i=1}^{n}{{{f}^{-1}}({{x}_{i}})}=f\left( \frac{1}{n}\sum\limits_{i=1}^{n}{{{x}_{i}}} \right)\] (ii) \[\sum\limits_{i=1}^{n}{{{f}^{-1}}}({{x}_{i}})=\sum\limits_{i=1}^{n}{{{x}_{i}}},\] where \[{{f}^{-1}}\] denotes the inverse of f. The value of \[\frac{{{x}_{1}}+{{x}_{2}}+...+{{x}_{n}}}{n}=\]

• A. 1
• B. 2
• C. 3
• D. 4