lean_workbook_plus_17522

What if the function $g(a)$ was defined as $g(a) = 0$ for all $a$ in the interval $[0, 1]$? Show that $g$ is continuous on that interval, but there is no $a \in [0, 1]$ such that $g(a) = \frac{1}{a} + \frac{1}{1-a}$.