Question

The domain of the function
$f\left(x\right)={\log }_{10}\left\{1-{\log }_{10}\left(x^2-5x+10\right)\right\}$ is

• A. $\left(0,\infty \right)$
• B. $\left(0,5\right)$
• C. $\left(-\infty ,0\right)$
• D. None

Answer 1

The correct option is A $\left(0,\infty \right)$

$f\left(\right)=\log \{1-{\log }_x(x^2-5x+10)\}$

For existance of $f\left(x\right),1-{\log }_{10}{x}^2-5x+10)>0$

$\Rightarrow {\log }_{10}{x}^2-5x+10)<1$

$\Rightarrow x^2-5x+10<10$ (1)

$\Rightarrow x^2-5x+10<10$

$\Rightarrow x^2-5x<0$

$\Rightarrow x\in (0,5)$

$D\left(f\left(x\right)\right)=(0,5)$