Can $\mathbb A=\{f(x)\mid x\in\mathbb R\}$ be shortened as $\mathbb A=f(\mathbb R)$?

Question

Can $\mathbb A=\{f(x)\mid x\in\mathbb R\}$ be shortened as $\mathbb A=f(\mathbb R)$?

I saw this notation in the IMO olympiad training materials (the solution to the Problem 16 (IMO 1999 Problem 6) here).

Because the source seems reliable, I believe the notation is correct, but can you confirm this?