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?

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

score 2 · Answer 1 · edited Jun 12 '20 at 10:38

2

Hint

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

edited Jun 12 '20 at 10:38

Community

answered Apr 10 '18 at 19:40

Delta-u

1 Answers1