Question

Does the inverse function of the following real valued function of real variable
exist ? Give reasons.
f(x)= [X]​

Answer 1

Given : f(x)=[x]

To Find : Does the inverse function  of real variable exist

Solution:

f(x)=[x]

[x]   = Greatest integer function

x = 1  => f(1)  = 1

x= 1.01  => f(1.01) = 1

x = 1.2 => f(1.2) = 1

x = 1.99 => f(1.99) = 1

f(1) =  f(1.2) but 1#1.2  Hence function is not one to one

As function is not one to one  so function  is not bijective  

A function is said to be invertible iff it is bijective

Since  function   is not bijective  

Hence the inverse does not exists

=>  the inverse function of the f(x)=[x] of real variable does not exist

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कारण  f(x)=|x|

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