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## Homework Statement

Is there a continuous function f:R->R such that f'(f(x)) = x ?

## Homework Equations

## The Attempt at a Solution

I've been working on this problem for quite some time now. I can see that, supposing there is such a function f, then [tex]f^{-1}(x) = f'(x)[/tex]. So we are looking for a function whose derivative is its inverse.

I'm trying to see what other information I can gather from the givens, but I'm pretty much clueless as to where to go from here. Any suggestions?