If $f: R \to R$ is defined by $f(x) =x-[x]-\large\frac{1}{2}$ for $x \in R,$ where $[x]$ is the greatest integer not exceeding x, then $\bigg \{x \in R: f(x) =\frac{1}{2}\bigg\}$ is equal to :

Question

(a) Z, the set of all integers

(b) N, the set of all natural numbers

(c) $\phi$, the empty set

(d) R