Question

Is the inverse of a function, always a function?

Answer 1

Yes, if a function is invertible- it has to be a one to one
So it's inverse would also have a one to one relation and consequently a function

Answer 2

iits an inverse cosign but yes it is a function

Answer 3

But there are exceptions
sin x is a periodic function, it has a many to one relation. Its inverse doesn't exist
But arcsin or\( \sin^{−1}x \) is defined with constraints on domain and range

Answer 4

No. Not always. For example the parabola y = x^2 is a function but its inverse x=y^2 is not a function.