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?

  • 3
    $\begingroup$ You want to assume $f$ is continuous, otherwise there are more exotic solutions. $\endgroup$ – Robert Israel Apr 10 '18 at 19:51
  • 1
    $\begingroup$ @ChristianF: The case $f(x)=0$ is already covered by the given function, by selecting $c=0$. $\endgroup$ – 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

| cite | improve this answer | |

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.