I am not sure of what exactly is asked in this question. Negation meant as $\neg$ is just a logical symbol, so it can be considered a "function of formulas", but this already seems off-road.
Definable functions are defined to have definable sets as domain, codomain, and graph.
In case negation has to be intended as complement, then the exercise is immediate using $\neg =$.
The question comes from exercise 4.6 of Kirby's Invitation to Model Theory (p.22).
I can confirm halrankard2's comment. You have to find a formula $\phi(x, y)$ in the language $\{+, 0\}$ such that $\mathbb{R} \models \phi(x, y)$ if and only if $y = -x$. This way the formula $\phi$ defines (the graph of) the function that sends $x$ to $-x$.
Hint: if $y = -x$ then what is $x + y$? In other words, what is the defining property of the negation of a real number?