2. Solved Papers
  3. JAMIA MILLIA ISLAMIA

JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2005

  • question_answer
         The function\[f(x)={{\cot }^{-1}}x+x\]increases in the interval:

    A)  \[(1,\infty )\]                   

    B)  \[(-1,\infty )\]

    C)  \[(-\infty ,\infty )\]                        

    D)  \[(0,\infty )\]

    Correct Answer: C

    Solution :

                    \[f(x)={{\cos }^{-1}}x+x\] \[\Rightarrow \]               \[f(x)=-\frac{1}{1+{{x}^{2}}}+1\]                 \[=\frac{{{x}^{2}}}{1+{{x}^{2}}},\]clearly,\[f(x)>0\]for all\[x\] So,\[f(x)\]increases in \[(-\infty ,\infty )\]


You need to login to perform this action.
You will be redirected in 3 sec spinner