Question

The set values of $x$ for which function $f\left(x\right)=x\ln x-x+1$

• A. $(1,\infty )$
• B. $(\frac{1}{e},\infty )$
• C. $[e,\infty )$
• D. $(0,1)\cup (1,\infty )$

Answer 1

The correct option is A $(1,\infty )$

$f\left(x\right)=x\ln x-x+1$

we use the formula

${\log }_{a}f\left(x\right)\Rightarrow f\left(x\right)>0$

$\Rightarrow x>0$

$\therefore x>0\Rightarrow (1,\infty )$