# Let a function $f:(0,\infty)\rightarrow (0,\infty)$ be defined by $f(x)=\left | 1-\frac{1}{x} \right |.$Then $f$ is:Option 1)  not injective but it is surjectiveOption 2)  both injective as well as surjectiveOption 3)neither injective nor surjectiveOption 4)injective only

One - One or Injective function -

A function in which every element of range of function corresponds to exactly one elements.

- wherein

A line parallel to x - axis cut the curve at most one point.

Curve of $f(x)=\left | 1-\frac{1}{x} \right |$

Option 1)

not injective but it is surjective

Option 2)

both injective as well as surjective

Option 3)

neither injective nor surjective

Option 4)

injective only

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