what is the condition for any function to coinside with its inverse function other than at line y=x?

Question

anonymous · Answer

it can be any identity function i spose

anonymous · Answer

?

binary3i · Answer

no

anonymous · Answer

sentence does not parse

mathmate · Answer

y=sqrt(x^2)

anonymous · Answer

The function must be one-to-one to have an inverse function (or it can be many-to-one with constraints)

across · Answer

Assume you have a function $f(x)$ whose inverse is $f^{-1}(x)$. If you define a function $g(x)=f(f^{-1}(x))$, you'll end up with a function $g(x)=x$ which lies on the line $y=x$.

mathmate · Answer

Oops, y=x^2 doesn't quite work, because it resembles the absolute function, and the inverse does not coincide with the function.

anonymous · Answer

can you rephrase the question?  you are getting several answers indicating that the question is not clear at all

mathmate · Answer

If f(f-1(x))=x, and f(x)=f-1(x), then
f(f(x))=x
would be a requirement.

anonymous · Answer

given a one to one function f, then 
$$f(a)=f^{-1}(b)$$ if 
$$a=b$$

binary3i · Answer

i asked is their any point for f(x) which is also on $$ f^{-1}$$ but not on line y=x if yes then what can you say about the function?