A) \[(0,\infty )\]
B) \[(-\infty ,0)\]
C) \[(-\infty ,\infty )\]
D) None of these
Correct Answer: A
Solution :
| Given \[f(x)=\log (1+x)-\frac{2x}{2+x}\] |
| \[f'(x)=\frac{1}{1+x}-\frac{(2+x)(2)-2x}{{{(2+x)}^{2}}}\]\[=\frac{1}{1+x}-\frac{4}{{{(2+x)}^{2}}}=\frac{{{(2+x)}^{2}}-4-4x}{(1+x){{(2+x)}^{2}}}\]\[=\frac{{{x}^{2}}}{(1+x){{(2+x)}^{2}}}>0\] for all \[x\in (0,\infty )\] |
| Thus, given function f(x) is increasing on \[(0,\infty )\]. |
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