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Let A = {x ∈ R : x is not a positive integer}. Define a function f : A  R as f(x)  = 2x/(x - 1), then f is : 

(1) surjective but not injective 

(2) injective but not surjective 

(3) neither injective nor surjective 

(4) not injective 

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The correct option (2) injective but not surjective  


Ratio of two linear polynomials 2x & (x – 1) isn't surjective even for domain being all real numbers (except 1). f(x) is injective though.

[considering all real numbers (except 1) as domain]

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