Novice question: how do you approach solving an equation like this?

Question

How do you find $f(x)$ if you know that: $$f(2x) = 2f(x) - f(x)^2$$

The result is: $f(x)=1-e^{cx}$ (where $c$ is an arbitrary constant).

What would be the steps to get to the result?

Answer 1

Hint

With $g(x)=1-f (x) $ you obtain: $$g (2x) =g (x)^2$$ You can then look at this