Q78 / 120 · VITEEE 2013 · Mathematics

The domain of the function $f(x)=\frac{1}{\log _{10}(1-x)}+\sqrt{x+2}$ is

  • A
    $]-3,-2.5[\cap]-2.5,-2[$
  • Correct answer
    B
    $[-2,0[\cup] 0,1]$
  • C
    $] 0,1[$
  • D
    None of the above

Solution

$x+2 \geq 0$, i.e., $x \geq-2$ or $-2 \leq x$ $\log _{10}(1-x) \neq 0$ $\Rightarrow 1-x \neq 1 \Rightarrow x \neq 0$ Again, $1-x>0$ $\Rightarrow 1>x \Rightarrow x < 1$ Combining all the results for values of $x$, we get $-2 \leq x < 0 \text { and } 0 < x < 1$

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

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