A) \[f(x)\] is increasing in \[(-\infty ,0)\]
B) \[f(x)\] is decreasing in \[(0,\infty )\]
C) \[f(x)\] is increasing m \[(1,\infty )\]
D) \[f(x)\] is decreasing in (0, 1)
Correct Answer: B
Solution :
\[f(x)=\left[ \begin{matrix} {{x}^{2}}-\ell n{{x}^{2}}, & x\ge 0 \\ -{{x}^{2}}-\ell n{{x}^{2}}, & x<0 \\ \end{matrix} \right.\] |
\[f'(x)=\left[ \begin{matrix} 2x-2/x, & x>0 \\ -\,2x-2/x, & x<0 \\ \end{matrix} \right.\] |
\[=\left[ \begin{matrix} \frac{2\,\,(x-1)\,\,(x+1)}{x}, & x>0 \\ \frac{-\,2({{x}^{2}}+1)}{x}, & x<0 \\ \end{matrix} \right.\] |
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