Inverse Functions

1.5 Inverse functions

Finding inverse functions informally
ex. 
Find the inverse of f(x) = x - 6.  Then verify that both are equal to the identity function

You can verify that both functions are equal to the identity because: 

 
 


Definition of the inverse of a function

let f and g be two functions such that
       for every x in the domain of g
and
      for every x in the domain of f
We can conclude from this that, the function g is the inverse of the function f
Verifying inverse functions algebraically

ex.  Show that the functions are inverse of each other
     and       


                                             
                                           
                                           



                                         
                                         
                                         
Testing for one-to-one functions
ex. is one to one


   
   
      
Therefore,

implies that

So, f is indeed a one-to-one functions


Finding the inverse of a function

-Alec