A) 1
B) 2
C) 3
D) 4
Correct Answer: A
Solution :
[a] \[\frac{{{f}^{-1}}({{x}_{1}})+{{f}^{-1}}({{x}_{2}})+...+{{f}^{-1}}({{x}_{n}})}{n}\] \[=f\left( \frac{{{x}_{1}}+{{x}_{2}}+...+{{x}_{n}}}{n} \right)\] and \[\frac{{{f}^{-1}}({{x}_{1}})+{{f}^{-1}}({{x}_{2}})+...+{{f}^{-1}}({{x}_{n}})}{n}\] \[=f\left( \frac{{{x}_{1}}+{{x}_{2}}+...+{{x}_{n}}}{n} \right)\] \[\Rightarrow f(\bar{x})=\bar{x},\] Where \[\bar{x}=\frac{{{x}_{1}}+{{x}_{2}}+...+{{x}_{n}}}{n}\] \[\Rightarrow {{\bar{x}}^{2}}+3\bar{x}-3=\bar{x}\Rightarrow {{\bar{x}}^{2}}+2\bar{x}-3=0\] \[\Rightarrow \bar{x}=-3,1\Rightarrow \bar{x}=1\,\,as\,\,\bar{x}>0\]You need to login to perform this action.
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