Given a function $g:\mathbb{R}\rightarrow \mathbb{R}$. Say I want to find a function $f:\mathbb{R}\rightarrow \mathbb{R}$ such that the integral over $f(x)g(x)$ is maximized under the constraint that $|f(x)| \leq 1$.
I would write that down, noting that $\mathbb{F}$ is a function space, as
$$ \begin{align} \max_{f \in \mathbb{F}} & \int_{-\infty}^{\infty} f(x) g(x) dx \,\, \text{ s.t.} \tag{1} \\ &|f(x)| \leq 1 \\ &x \in \mathbb{R} \,. \end{align} $$
Question: Is this notation ok? I.e. is it correct/good style to write $(1)$ like this?
EDIT: Corrected the equation.