Inverse Function

Date: 8/2/96 at 1:58:23
From: Alfred T Chu
Subject: Inverse Function

Dear Dr. Math,

I have a questions:

z(x) = 4x + 15. How do I find the inverse function of   z(x)?

Sincerely,

Alfred

Date: 8/6/96 at 10:56:53
From: Doctor Jerry
Subject: Re: Inverse Function

Dear Alfred,

You want the inverse function of z(x) = 4x+15. 

Usually, in inverse function questions, it is important to specify the 
domain of the function.  For the function z, I assume the domain is R, 
the set of all real numbers.  The function z gives y = z(x) values 
when x values are given. The function zinv gives x values when y 
values are given. So, suppose y = z(x) is given.  What value of x is 
required for this?

To determine x, we solve the equation y = 4x+5 for x.  I feel certain 
you can do this.  I find x = (y-5)/4.  So z inv(y) = (y-5)/4.  

Some persons prefer the variable of a function to be x, so they prefer 
to write zinv(x) = (x-5)/4 when describing the function zinv to 
another person. 

-Doctor Jerry,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/