- #1
Saracen Rue
- 150
- 10
Through experimental observations, I have found that the two functions ##f\left(x\right)=x^{a\left(a-x^3\right)}-a## and ##g\left(x\right)=a^{x\left(x-a^3\right)}-x## will always intersect at ##a## when ##x>0##. Is there a way to mathematically prove this? For instance, simultaneously solving the functions and simplifying the answer down to ##x=a## (Note: the functions sometimes also intersect at other locations besides ##[a, f(a)]##)