(From a question at HNUE High School for the Gifted)
Let $$f(x) = |a|^{bx}-|b|^{ax}\\g(x) = abx$$Such that $a$ and $b$ are real numbers.
What are the conditions needed for $f(x)$ and $g(x)$ to intersect at three separate points? And in that scenario, what is the total area of the two areas bounded by $f(x)$ and $g(x)$?
My current work so far assumes that $b = k \cdot A$ ($k$ is some integer), yet the upper bound given $a<0$, for some reason, is $$k> \frac{-25\cdot a}{16}$$ I still haven't found a general answer for both questions, but this specific upper bound makes me curious.
