Q48 / 120 · VITEEE 2010 · Mathematics

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
    $(-\infty,-1]$
  • Correct answer
    D
    $(-\infty,-1] \cup[1, \infty)$

Solution

$f(x)=\sqrt{\log _{10} x^{2}}$ is real, if $$ \begin{array}{l} \log _{10} x^{2} \geq 0 \\ \Rightarrow x^{2} \geq 1 \\ \Rightarrow x < -1 \text { and } x>1 \\ \Rightarrow x \in(-\infty,-1] \cup[1, \infty) \end{array} $$

Hence, the correct answer is option: 'D'.

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