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  • Confused! kindly explain, - Let a functionbe defined by Then is: - Sets, Relations and Functions - JEE Main

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 surjective

  • Option 2)

     

    both injective as well as surjective

  • Option 3)

    neither injective nor surjective

  • Option 4)

    injective only

Answers (1)

best_answer

 

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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