Q.Find the domain and range of the exponential function $f(x) = e^x$ and the logarithmic function $g(x) = \log_e x$, and state how the two functions are related.

Step 1: $f(x)=e^x$ is defined for every real $x$ (domain $\mathbb{R}$) and, since $e>1$, is always strictly positive and takes every positive value; range $=(0,\infty)$.

Step 2: $g(x)=\log_e x$ is defined only when its argument is positive, so domain $=(0,\infty)$; as $x$ ranges over all positive reals, $\log_e x$ takes every real value; range $=\mathbb{R}$. …

Recall the domain/range of the exponential function and of the logarithmic function separately, then note …