can a function be inverse of it self if yes than state its property?

Question

anonymous · Answer

yeah it can like f(x)=x

anonymous · Answer

Is there a specific domain for these functions you are considering? 

If not, you can use:$$f:\mathbb{C}\longrightarrow \mathbb{C}$$$$f(z) = \bar{z}$$

The complex conjugate function.  This is a bijective function over the complex numbers, so it has an inverse.  and its easy to see that:$$f(f(z)) = f(\bar{z}) = z$$so it is its own inverse.

anonymous · Answer

In general if f(x)=f^-1(x) ,then f(f(x))=x

binary3i · Answer

what i know is it should be symmetric about the line y=x

anonymous · Answer

Or you can find a matrix A such that:$$A^2 = I$$Then create a linear transformation:$$T:\mathbb{R^n}\longrightarrow \mathbb{R^n}$$$$T(x) = Ax$$That would also do the job. It just depends on what your domain should be.  Real Numbers? Vectors?  complex numbers?  Gotta be a little specific.

anonymous · Answer

The inverse of a function is basically obtained by replacing x with y and y with x in other words taking image about the line y=x so on reflection if you get f(x) itself i.e, symmetric abt y=x then it is its own inverse.