If we are given a formula for a 1-1 function 
as y=f(x)
then there is an algebraic method that attempts to find a formula for 
. Whether or not the method is successful usually depends on whether
or not the algebraic steps can be carried out. The basic idea is this. Since
a point (x,y) in the graph of f satisfies the equation y=f(x), the
point (y,x) in the graph of should satisfy the equation x=f(y).
The only problem is can you solve this for y. That just means can you
algebraically solve x=f(y) for y in terms of x. If you can, you will
have 
, the formula for the inverse function. So the steps are:
(1) write down y=f(x)
(2) switch x and y to get x=f(y)
(3) solve for y to get
Here's a simple example: Let 
a 1-1 and onto function from R
to R. Here are the steps.
(1) 
(2) 
(3)solving for y:
So we get 
.