Question

If $f\left(x\right)=\sqrt{{\log }_{10}{x}^2}$, then the values of $x$ for which $f\left(x\right)$ is real is/are

• A. $2$
• B. $-5$
• C. $0$
• D. $0.5$

Answer 1

Answer: (A), (B)

The correct options are
A $2$
B $-5$

$f\left(x\right)$ is real when ${\log }_{10}{x}^2>0$
$\Rightarrow x^2>1$
Therefore, $x>1$ and $x<-1$
Clearly $x=2$ and $x=-5$ satisfies this conditions.
Hence, option A and B.