Consider the function $f,g:\mathbb C \rightarrow \mathbb C$ defined by $f(z) = e^z, g(z) = e^{iz}$. Let $S = \{z \in \mathbb C: \mbox{Re }z \in [-\pi, \pi] \}$. Then

- $f$ is an onto entire function.
- $g$ is a bounded function on $\mathbb C$.
- $f$ is bounded on $S$.
- $g$ is bounded on $S$.