give an example of two increasing functions whose product is not increasing

Answer 1

f(x)=i x, g(x)=i(x^2) where i is the sqrt(-1) for x>0

Answer 2

without delving into complex numbers, maybe something like

f(x) = e^2x
g(x) = -e^-x
(fg)(x) = -e^x, which is decreasing