Question

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

• A. injective only
• B. not injective but it is surjective
• C. neither injective nor surjective
• D. both injective as well as surjective

Answer 1

The correct option is A injective only

NOTE: It is a bonus question.
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$f\left(x\right)=|1-\frac{1}{x}|$
For $x=1$
$f\left(x\right)=|1-\frac{1}{1}|=0$
But the co-domain is $(0,\infty )$ which is not including $0$
So $f\left(x\right)$ is not a function.