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

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?

• You want to assume $f$ is continuous, otherwise there are more exotic solutions. – Robert Israel Apr 10 '18 at 19:51
• @ChristianF: The case $f(x)=0$ is already covered by the given function, by selecting $c=0$. – celtschk Apr 10 '18 at 20:06

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