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Let a function

Question:

Let a function $f:(0, \infty) \rightarrow(0, \infty)$ be defined by

$f(x)=\left|1-\frac{1}{x}\right| .$ Then $f$ is :-

  1. Injective only

  2. Not injective but it is surjective

  3. Both injective as well as surjective

  4. Neither injective nor surjective


Correct Option: , 2

Solution:

$f(x)=\left|1-\frac{1}{x}\right|=\frac{|x-1|}{x}=\left\{\begin{array}{cc}\frac{1-x}{x} & 0

$\Rightarrow f(x)$ is not injective

but range of function is $[0, \infty)$

Remark: If co-domain is $[0, \infty)$, then $f(x)$ will be surjective

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