Question

Function $f\left(x\right)=x-\log x$ is monotonic decreasing when-

• A. $x\in (0,1)$
• B. $x\in (-1,1)$
• C. $x\in (1,\infty )$
• D. None of these

Answer 1

The correct option is A $x\in (0,1)$

$y^{\prime }\left(x\right)$
$=1-\frac{1}{x}$
Hence for it to be increasing
$y^{\prime }\left(x\right)>0$
Or
$x>1$
Hence it is an increasing function for all $x>1$.
Hence it will be decreasing in $R^{+}-(1,\infty )$
$=(0,1)$
Since input of logarithmic function cannot be negative.