Let A = {x\epsilon } R : x is not a positive integer. Define a function f:A\rightarrow R asf(x) = 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)
A admin

 

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.


Option 1)

 

injective but not surjective

Option 2)

 

neither injective nore surjective

Option 3)

 

not injective

Option 4)

 

surjective but not injective

Exams
Articles
Questions