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 .

Fri Aug 9 15:39:38 PDT 1996