क्या निम्नलिखित वास्तविक चर के वास्तविक-मानित फलन का प्रतिलोम फलन प्राप्त होगा ?
कारण दें।
f(x)=|x/
Answers
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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