Whoops, my assessment was for
x*(1-exp(-x)) <= 1 , no
t x*(1+exp(-x)) <= 1.
So it turns out that C2 is concave for x <= 2 and convex for x >= 2. That means that if C1 is
1 <= x <= 2 , then C2 is non-convex in the domain restricted by C1. Therefore the problem is non-convex, period, and it can not be entered into CVX.
Actually, C2 is only feasible for x <= 0.65905, so if the lower bound of C1 is not at least that low, the problem isn’t even feasible, quite apart from whether it can be entered into CVX.