For a discussion of the topic see http://math.eretrandre.org/tetrationforu...11#pid2411
Conjecture
Let \( b=\sqrt{2} \). Every real function \( f \) on \( (-2,\infty) \) that satisfies:
\( f(0)=1 \)
\( f(x+1)=b^{f(x)} \)
\( f(-f(x))=-x \)
is not continuous at any point.
Conjecture
Let \( b=\sqrt{2} \). Every real function \( f \) on \( (-2,\infty) \) that satisfies:
\( f(0)=1 \)
\( f(x+1)=b^{f(x)} \)
\( f(-f(x))=-x \)
is not continuous at any point.