Assume functions $f$ and $g$ are continuous on the interval $[a,b]$. Show that the set
$E = \{x \in [a,b] : f(x) + g(x) \leq 0 \}$ is compact.
Assume functions $f$ and $g$ are continuous on the interval $[a,b]$. Show that the set
$E = \{x \in [a,b] : f(x) + g(x) \leq 0 \}$ is compact.