Question

क्या निम्नलिखित वास्तविक चर के वास्तविक-मानित फलन का प्रतिलोम फलन प्राप्त होग
कारण
f(x)=|x|
​

Answer 1

Given : f(x)=|x|  

To Find : क्या   वास्तविक चर के वास्तविक-मानित फलन का प्रतिलोम फलन प्राप्त  होगा

Solution:

f(x) = | x|

f(x) = x   if  x  ≥ 0

=> x = f(x)  if  x  ≥ 0

f(x) = - x   if  x  < 0

=> x = - f(x)  if  x  < 0  

x =2

=> f(x) = 2

x = - 2

=> f(x) = 2

f(2) =  f(-2) but 2#-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

प्रतिलोम फलन     संभव नहीं

वास्तविक चर के वास्तविक-मानित फलन का प्रतिलोम फलन प्राप्त नहीं होगा  

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