# Independence of two functions

1. Sep 14, 2008

### Heirot

When are to functions y1 = f1(x) and y2 = f2(x) independent? It would apper never, because, we can always write x = f1-1 (y1), and therefore y2 is a function of y1. Every function is dependent of any other function. Generally, dy1/dy2 != 0 for arbitrary functions y1 and y2. Is this reasoning correct?

2. Sep 14, 2008

### Ben Niehoff

We can, however, talk about linearly-independent functions: namely, functions with vanishing Wronskian.

3. Sep 14, 2008

### Defennder

I can't figure out what the OP is saying about independent functions. It's not the same as the concept of linear independence, is it?

4. Sep 14, 2008

### Mute

It's when the Wronskian doesn't vanish that the two functions are linearly independent.

5. Sep 15, 2008

### HallsofIvy

I have no idea what you are saying! Do y1, y2, x1, x2 just represent numbers? What, then, is the difference between saying y1= f1(x1) and just y= f1(x)? And, of course, what do you mean by "independent"? Apparently you don't mean "linear independence". Before anyone can tell you whether or not "any two functions are not independent" you will have to say what you mean by two functions being "independent"!