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 $\log _{10} x^{2} \geq 0$
$\Rightarrow x^{2} \geq 1$
$\Rightarrow x<-1$ and $x >1$
$\Rightarrow x \in(-\infty,-1] \cup[1, \infty)$