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Formula for inverse function

If we are given a formula for a 1-1 function tex2html_wrap_inline22 as y=f(x) then there is an algebraic method that attempts to find a formula for tex2html_wrap_inline26 . 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 tex2html_wrap_inline26 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 tex2html_wrap_inline48 , 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 tex2html_wrap_inline48

Here's a simple example: Let tex2html_wrap_inline62 a 1-1 and onto function from R to R. Here are the steps.

(1) tex2html_wrap_inline68

(2) tex2html_wrap_inline70

(3)solving for y:


So we get tex2html_wrap_inline74 .

Dan Rinne
Fri Aug 9 15:39:38 PDT 1996