Maths-
General
Easy

Question

Functionf colon Z rightwards arrow Z comma f(x) = 2x + 1 is-

  1. one-one onto    
  2. one-one     
  3. many one onto    
  4. many one into    

hintHint:

A function is said to be bijective or bijection, if a function f: A → B satisfies both the injective (one-to-one function) and surjective function (onto function) properties. It means that every element “b” in the codomain B, there is exactly one element “a” in the domain A.

The correct answer is: one-one


    Given :  f colon Z rightwards arrow Z comma f(x) = 2x + 1
    For, f(x) = 2x + 1 is an one - one function but not onto.
    f is one - one as forf left parenthesis x subscript 1 right parenthesis space space equals space f left parenthesis x subscript 2 right parenthesis space rightwards double arrow x subscript 1 space equals space x subscript 2
B u t space f space i s space n o t space o n t o.
A s space f o r space e x a m p l e space 2 space element of t h e space c o minus d o m a i n space o f space f.
N o w space f o r space 2 space equals space 2 x space plus space 1
o r. space x space equals space 1 half space n o t space a n space e l e m e n t space o f space Z
S o space t h e r e space e x i s t s space o n e space s u c h space p o i n t space i n space t h e space c o space d o m a i n space o f space t h e space f u n c t i o n space w h i c h space h a v e space n o space p r e space i m a g e space i n space t h e space d o m a i n space o f space t h e space f u n c t i o n.
S o. space f space i s space n o t space o n t o
f space i s space a space o n e minus o n e space f u n c t i o n.

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