One -One function

1.One - One function or Injection:-

  • If every element of the domain is mapped with unique elements of Range.
  • If the domain has 'm' elements then range must have 'n' elements such that                         n\geq m

let |A| = n and |B| = m then the total number of one -one function from A to B is:- 

       $^m P_n$.

 

example:  Is f(x) = x^{2} is One -One function?

Solution:-

If anywhere you are asked about one-one function what you need to do is like this:

f(x) = x^{2}

f(y)=y^{2}

now equate them:

f(x) = x^{2} =f(y)=y^{2}

or 

x^{2} =y^{^{2}}

x^{2} - y^{2} =0

(x+y)(x-y) =0

or

x=y or x=-y Since we are getting two value for x ,so it is not One -One function.

 

 

 

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