Question

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

• A. $[-1,1]$
• B. $[1,+\infty )$
• C. $(-\infty ,-1]$
• D. $(-\infty ,-1]\cup [1,+\infty )$

Answer 1

The correct option is D $(-\infty ,-1]\cup [1,+\infty )$

$f\left(x\right)=\sqrt{{\log }_{10}{x}^2}$
is real when ${\log }_{10}{x}^2\ge 0$
$\Rightarrow x^2\ge 1$
$\Rightarrow x\in (-\infty ,-1]\cup [1,+\infty )$
Ans:D