Question

If $f(x)=\sqrt{{\log }_{10}{x}^2}$ . The set of all values of $x$ for which $f(x)$ is real , is

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

Answer 1

Answer: (D)

$f(x)=\sqrt{{\log }_{10}{x}^2}$ is real
If ${\log }_{10}{x}^2\ge 0$
$\Rightarrow x^2\ge 1$
$\Rightarrow x<-1$ and $x>1$
$\Rightarrow x\in (-\infty ,-1]\cup [1,\infty )$