While studying inverse trigonometric functions ,a thought struck me that inverse function like $sin^{-1} {x}$ and $cos^{-1} {x}$ have domain [-1,1] but what about rest of the Real space/Real line
Can't we have a function that in a certain domain be inverse of some function and outside that certain domain(or to some extent) be the inverse of another function/functions?
Or atleast be inverse of n = 2 functions?
Is there any example of any of them?
If so what are the generalized properties of such functions?(their derivatives,behaviours,etc...)
Where can I look for more information?
ANy well known applications of such functions outside mathematical research say in Physics/Engineering? and why they are incorporated as such?(what property makes the feasible for such branches)
I s there any property/axiom/theorem barring to do so?(construct such f(x)s)
IS there any branch of maths exist that especially analyses this kind of function?
a function that ... outside that certain domain
A function is always defined on acertain domain
. It's not even defined outside it, let alone be the inverse of some other function (or not). $\endgroup$ – dxiv Oct 24 '16 at 6:15inverse of n functions
makes no sense. $\endgroup$ – dxiv Oct 24 '16 at 6:22