Contrast vs. Brightness question
Write down brightness and contrast as functions that act on a single gray-scale pixel. As you said, brightness is $b(x) = x + \alpha$ and contrast is $c(x) = \beta(x - x_\text{mean}) + x_\text{mean}$ or something similar. Now all you need to show is that $b \circ c \neq c \circ b$.