Q39 / 90 · JEE Main 2019 (11 Jan Shift 2) · Mathematics

Let a function $f:(0, \infty) \rightarrow(0, \infty)$ be defined by $f(x)=\left|1-\frac{1}{x}\right| .$ Then $f$ is :

  • A
    not injective but it is surjective
  • B
    injective only
  • C
    neither injective nor surjective
  • Correct answer
    D
    None of the above

Solution

$f:(0, \infty) \rightarrow(0, \infty)$ $f(x)=\left|1-\frac{1}{x}\right|$ is not a function $\because f(1)=0$ and $1 \in$ domain but $0 \notin$ co-domain Hence, $f(x)$ is not a function.

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

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