The interval in which the function $f$ defined by $f(x) = e^x$ is strictly increasing, is:

$(-\infty, \infty)$

The correct answer is Option (3) → $(-\infty, \infty)$ ##

$y = e^x \Rightarrow \frac{dy}{dx} = e^x$

In the domain $(\mathbb{R})$ of the function, $\frac{dy}{dx} > 0$, hence the function is strictly increasing in $(-\infty, \infty)$.