inverse function
- From: patrol_boat@xxxxxxxxxxx
- Date: Sat, 2 May 2009 11:40:53 -0700 (PDT)
The following definition of inverse functions has me confused:
f(y) = x <==> f^-1(x) = y
What bothers me is that I'm unable to relate the definition to the
practice of finding the inverse of a function.
For example, most functions are named with x as the domain element.
But f(x) isn't used in the definition.
Ex. find the inverse of the simple one-to-one polynomial f(x) = y = x
+1.
First, should I consider f(x) in the example as f(y) or as f^-1(x) in
the definiition?
My biggest question: The equivalence means that both equations
determine the same set of points (y,x), right?. But x is the *input*
of f^-1, so wouldn't f^-1 determine the points (x,y)? If the functions
f and f^-1 are equivalent, then how is the definition even stating the
inverse, and how is using the definition getting you the inverse?
I know the mechanical procedure for finding the inverse of many
functions, but relating it to the definition is where I'm totally
confused.
f(x) = y = x + 1
x = y -1 (solve for x)
y = x - 1 ("swap" x and y)
f^-1(x) = x - 1
.
- Follow-Ups:
- Re: inverse function
- From: Virgil
- Re: inverse function
- From: Mariano Suárez-Alvarez
- Re: inverse function
- Prev by Date: Re: d|a[n]
- Next by Date: Re: exercise on Mersenne numbers (Crandall & Pomerance)
- Previous by thread: Minimal Polynomials for Tangents Revisited
- Next by thread: Re: inverse function
- Index(es):
Relevant Pages
|
