Computable function $f = \Theta(g)$ with $g$ uncomputable This question most likely has a simple answer; however, I do not see it.

Let $g:\mathbb{N} \rightarrow \mathbb{N}$ be an uncomputable function and $c$ a positive real number. Can there be a computable function $f : \mathbb{N} \rightarrow \mathbb{N}$ such that, for all $n$ large enough: $g(n) \leq f(n) \leq c \cdot g(n)$ (that is $f(n) = \Theta(g(n)$)?
Sure: just take g(n) = n + halt(n) (where halt(n)=1 if TM number n halts, and 0 ow).