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  4. The function f(x)= log (1+x)-(2 x/2+x) is increasing on

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Q. The function $f(x)=\log (1+x)-\frac{2 x}{2+x}$ is increasing on

KCETKCET 2022Application of Derivatives

Solution:

$f^{\prime}(x)=\frac{x^{2}}{(x+1)(2+x)^{2}}>0$
$x+1>0 \Rightarrow x>-1$