How to express a function as a function of another function?

  • Thread starter mnb96
  • Start date
  • #1
713
5
Hello,

I would like to know how I could approach the following problem. I am given two functions [itex]y=f(x)[/itex] and [itex]z=g(x)[/itex], and I would like to express the first function as a function of the second one: that is, [tex]y = h(z)[/tex], where h is not necessarily a linear function of z.

One explicit example could be: [tex]y=\frac{x}{a}[/tex] [tex]z=\frac{x}{a+b}[/tex]

where the goal is to find a function h such that [tex]y=h(z)[/tex]
 

Answers and Replies

  • #2
tiny-tim
Science Advisor
Homework Helper
25,832
251
hello mnb96! :smile:

invert g (if you can) …

x = g-1(z)

f(x) = f(g-1(z)) :wink:
 
  • #3
713
5
Ups...:)

You are right. When the inverse for g exists, it is pretty easy. Thanks.
I was wondering if it is still possible to do something when an inverse does not exist, although this goes slightly beyond the original question.
 
  • #4
tiny-tim
Science Advisor
Homework Helper
25,832
251
I was wondering if it is still possible to do something when an inverse does not exist, although this goes slightly beyond the original question.
it'd have to be a pretty weird function not to have at least a local inverse :wink:
 
  • #5
53
0
it'd have to be a pretty weird function not to have at least a local inverse :wink:
Indeed... but while they may have a inverse, it may be hard (or even impossible) to write down this inverse function... unless "cheating" is allowed, like using functions like Maple's RootOf( f(x) ) ...
 
  • #6
tiny-tim
Science Advisor
Homework Helper
25,832
251
Indeed... but while they may have a inverse, it may be hard (or even impossible) to write down this inverse function...
but we can still write it as g-1 :wink:
 

Related Threads on How to express a function as a function of another function?

Replies
6
Views
652
Replies
5
Views
729
Replies
3
Views
412
  • Last Post
Replies
19
Views
3K
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
3
Views
1K
Replies
11
Views
2K
Top