# Let $A = {x\epsilon }$ R : x is not a positive integer. Define a function $f:A\rightarrow R$ as$f(x) = 2x/x-1,$then f is:Option 1)  injective but not surjectiveOption 2)  neither injective nore surjectiveOption 3)  not injectiveOption 4)  surjective but not injective

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.

$f(x) = \frac{2x}{x-1}$

This can be written as

$\\f(x) =2 \left (1 + \frac{1}{x-1} \right )\\ f'(x) = -\frac{2}{(x-1)^2}$

$\Rightarrow$f is one-one i.e injective but not surjective.

Option 1)

injective but not surjective

Option 2)

neither injective nore surjective

Option 3)

not injective

Option 4)

surjective but not injective

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