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If a function is bijective, then its inverse exists. Is there any example that inverse of a function exists but the original function is not bijective?
However, why is x^2 not bijective if we define the domain containing zero(like x=>0)? It is a continous function so isn't it bijective at this interval though being not strictly increasing? ThanksA function can be locally bijective, so it's inverse exists only in some finite interval.
For example [tex]x^{2}[/tex] is not a bijective in any interval containing x=0 (since f'(0)=0) but if you restrict yourself to x>0, then you off course have the inverse
[tex]f(x)=\sqrt{x}[/tex] or in x<0 the inverse is [tex]f(x)=-\sqrt{-x}[/tex].
Thanks a lot! It may be a typo in my textbook.
However, why is x^2 not bijective if we define the domain containing zero(like x=>0)? It is a continous function so isn't it bijective at this interval though being not strictly increasing? Thanks