Consider $f: \mathbb{R} \to \mathbb{R}$ such that $f(x) = \frac{1}{x^2 +1}$ and $g: \mathbb{R} \to \mathbb{R}\times \mathbb{R}$ given by $g(x) = (3x, x^2)$.

I was asked to find the 'formulas' of $f \circ f$ and $g \circ f$ but I am unsure what exactly it would mean by formulas in this instance? I understand that with composite functions you solve them by doing the inner function and then the outer by: $f(g(x))$ is this what I have to do in this case?