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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 :

(a) Z, the set of all integers

(b) N, the set of all natural numbers

(c) $\phi$, the empty set

(d) R

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(c) $\phi$, the empty set
answered Nov 7, 2013 by pady_1

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