Answer
See explanation.
Work Step by Step
(a) $g(x)=e^{2 x}$ , $f(x)=e^{x}$ are positive and increasing everywhere, so the quotient $e^{-x}=(f / g)(x)$ is then decreasing everywhere
(b) $g(x)=e^{x}$ and $f(x)=e^{x}$ are positive and increasing everywhere, so the quotient $0=(f / g)(x)$ is then constant everywhere.
(c) $g(x)=e^{x}$ , $f(x)=e^{2 x}$ are positive and increasing everywhere, so the quotient $(f / g)(x)=x$ is then increasing everywhere.
