Q41 / 160 · AP EAMCET 2005 · Mathematics

$\{x \in R:[x-|x|]=5\}$ is equal to

  • A
    R, the set of all real numbers
  • Correct answer
    B
    $\phi$, the empty set
  • C
    $\{x \in R: x < 0\}$
  • D
    $\{x \in R: x \geq 0\}$

Solution

Let $f(x)=\{x \in[R:(x-|x|]=5\}$ $f(x)=0$ for $x \geq 0$ and $f(x) < 0$ for $x < 0$ $\Rightarrow$ no value of $x$ is satisfying the relation $\therefore \quad f(x)=\phi$

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

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