Re: Move to the other side and change the sign

Sharon Smith (ssmith@ADMIN1.AUGUSTA.TEC.GA.US)
Mon, 3 Feb 1997 10:32:45 -0500

I start my discussion for finding the inverse by writing the procedures for
putting one's shoes on in the morning and then writing the steps for taking
them off in the evening. You can expand this method to other simple 1 to 1
functions i.e. y = x3 - 5 ----> inverse would add 5 and take the cube root.
On a different level ---One of my Intermediate Algebra students in Minnesota
noticed there is a pattern between functions and their inverses of the form
y = (2x + 3)/(5x - 4)
We proved it for the 'generic form' ,y = (ax + b)/(cx + d),and named it a
theorem after him.

PM 2/2/97 EST, you wrote:
>A posting from G. Matthews talks about undoing operations to solve
>equations. I like this idea.
>
>In fact, it is one of the ways in which I introduce finding the
>formula for the inverse of certain functions.
>
>For example, given f(x) = 5x + 1, this says that to find the value of
>f(x), start with x, multiply by 5, then add 1 to the result.
>
>Since the inverse of a function "takes a value back from whence it
>came" we want to undo the above.
>
>To undo
> start with x, multiply by 5, then add 1 to the result,
>take the result, and
> subtract 1, then divide this by 5. (read the line above from
>right to left).
>Therefore the inverse function is
> f-1(x) = (x - 1)/5
>
>This works well for linear functions, and I don't try to go further
>with it. But it's another way to view the inverse of a function.
>
>Phil Mahler
>Middlesex CC
>Bedford, MA
>
>
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Sharon Smith
Augusta Technical Institute
Math Instructor
Isa 43:1-3
email ssmith@augusta.tec.ga.us
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