If f is continuous function for all x ∈ R and f(f(x))=1+x, then find value of f'(1).
An example of such a function (or possibly the only one) is f(x) = x + 1/2. Then f'(1) = 1, and in fact f'(x) = 1. If there's a unique solution, this is it.
In trying for an alternative, say f(x) = x + sin(x/(2*pi))+1/2. At first glance this would seem like an alterative, but in fact does not iterate into f(f(x))=x+1.
I'll stand by f'(1) = 1, in accordance with f(x) = x + 1/2.
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Posted by Charlie
on 2025-05-07 08:16:22 |
The solution, assuming it's unique
