Question 1190839

a) Define a function:

A function is a relation for which each value from the set the first components of the ordered pairs is associated with exactly one value from the set of second components of the ordered pair.


b) Define an inverse function:

Inverse function is represented by {{{f^-1(x)}}} with regards to the original function {{{f (x)}}}and the domain of the original function becomes the range of inverse function and the range of the given function becomes the domain of the inverse function. 


c) Given a function {{{f(x)}}}, when does {{{f^-1(x)}}} exist?

For any inverse to exist, function has to be one-one onto, i. e. bijective. 
The inverse exists when we can get back to an {{{x}}} given a {{{y}}}.