Consider the following function: $$f\left(x,y\right) = -x\cdot\ln\left( 0.5\right) - \left( y-x \right)\cdot\ln\left( 1-0.5e^{-x}\right) - \left( b-y \right)\cdot\ln\left( 1-0.5e^{-y}\right)$$ where $x$ and $y$ are subject to constraints $1 \leq x < y < b$. Note $b$ is a constant.
Show this function is quasiconvex over the given domain.
I've tried the level set approach but am having difficulty reasoning about the convexity of the resulting domains so am at a bit of an impasse. It seems to me that the answer must have something to do with the fact that the sum of quasiconvex functions on different domains is still quasiconvex.