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Let A = {x\epsilon } R : x is not a positive integer. Define a function f:A\rightarrow R asf(x) = \frac{2x}{x-1} then f is:

Option 1) injective but not surjective

Option 2) neither injective nore surjective

Option 3) not injective

Option 4) surjective but not injective

Answers (1)

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}

\Rightarrowf is one-one i.e injective but not surjective.

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