How to show that $ x_f $, a single zero of (possibly downward-slopping) function $ f(\alpha, \beta, x) $ is greater than $ x_g $, a single zero of other (possibly downward-slopping, too) function $ g(\alpha, \beta, x) $, for some fixed values of $ \alpha, \beta\in\mathbb{R}^+ $?
I know that both $ x_f $ and $ x_g $ are greater than 0. One problem is that functions can't be expressed in terms of elementary functions, and I have to deal with parameters $ \alpha, \beta $.