Q247 / 270 · NDA 2023 (Phase 1) · Mathematics

What is the range of the function $f(x)=x+|x|$ if the domain is the set of real numbers?

  • A
    $(0, \infty)$
  • Correct answer
    B
    $[0, \infty)$
  • C
    $(-\infty, \infty)$
  • D
    $[1, \infty)$

Solution

$f(x)=x+|x|$ when $x \lt 0, f(x)=x-x=0$ when $x \geq 0, f(x)=x+x=2 x$ $\therefore \quad f(x) \in(0, \infty)$

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

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