A) \[(1,\infty )\]
B) \[(-1,\infty )\]
C) \[(-\infty ,\infty )\]
D) \[(0,\infty )\]
Correct Answer: C
Solution :
\[f(x)={{\cot }^{-1}}x+x\] \[\Rightarrow \] \[f'(x)=-\frac{1}{1+{{x}^{2}}}+1\] \[=\frac{{{x}^{2}}}{1+{{x}^{2}}},\]clearly\[f'(x)>0\]for all\[x\]. So,\[f(x)\]increases in\[(-\infty ,\infty )\].
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