Is the sentence
A is bounded above by B, independent of C.
correct? I am not sure whether it should be independently instead of independent.
I am sorry for asking this here instead of ell.stackexchange.com, but in my experience I get more competent answers here for questions like this one.
More precisely, $A$ is a function $f_{C}(x)$ and $B$ is a function $g(x)$ and I want to express the mathematical statement $$ f_{C}(x)\leq g(x) \quad \forall x\forall C $$ in a part of my manuscript where I would like to avoid this kind of formalism. The sentence would thus be
We show that $f_{C}$ is bounded above by $g$, independent of C.