# Finding unknown functions

1. Sep 16, 2004

### Kerbox

Say you get a problem like this:
Find f(x) and g(x) when f(g(x))=|sin(x)| and g(f(x))=sin^2(sqrt(x)),
and Domain_f=R, Domain_g=[0,-> >

How would you approach to solve this, or do you have to keep guessing until you find two functions that fits?

2. Sep 16, 2004

### arildno

You'll have to keep guessing until you see:
f(x)=sqrt(x)
g(x)=sin^2(x)
Are you sure about the domains?

3. Sep 16, 2004

### Kerbox

I was looking for an algorithm or something that would work, when the example wasnt as simple as this one. When alot of simplifying had been done to the expressions for example.

And of course, the domains are reversed. Sorry about that.

4. Sep 16, 2004

### arildno

No, there are no general solve-all techniques for functional equations
(where your unknowns are functions, rather than some numbers, for example)

5. Sep 16, 2004

### geometer

Of course mathematicians don't want to be perceived as just guessing at possible answers so they have termed this method "solution by inspection."

6. Sep 16, 2004

### arildno

7. Sep 16, 2004

### Tide

Hey, trial and error is a perfectly valid mathematical method! Of course it's not always the most efficient path to a solution. :-)

8. Sep 17, 2004

### arildno

Well, it's a perfectly valid praxis, don't know about method though..