A) \[(1,\infty )\]
B) \[(-1,\infty )\]
C) \[(-\infty ,\infty )\]
D) \[(0,\infty )\]
Correct Answer: C
Solution :
A function f(x) is said to be increasing function, if \[f'(x)\ge 0\]. Since, \[f(x)={{\cot }^{-1}}x+1\] On differentiating w.r.t. x, we get \[f'(x)=-\frac{1}{1+{{x}^{2}}}+1=\frac{{{x}^{2}}}{1+{{x}^{2}}}\] Hence, \[f'(x)\] increasing function since \[f'(x)\ge 0\]for all \[x\].
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