Upgrade to access all content for this subject

Suppose $f(x)$ is a function defined for all real numbers. We say the number $a$ is a fixed point of $f(x)$ if, and only if

$bf(a) = f(ab)$.

$f(a) = a$.

$f'(a) = 0$.

For all $x: f(x + a) = f(x)$.