Question

lf $f$ : $R\to R$ is defined by $f\left(x\right)=x-\left[x\right]-\frac{1}{2}\forall x\in R$ $\left[x\right]$ is the greatest integer not exceeding $x$ then $\{x\in R:f(x)=\frac{1}{2}\}=$

• A. the set of all integers
• B. $N$, the set of all natural numbers
• C. $\varphi$, the empty set
• D. R

Answer 1

Answer: (C)

$\varphi$, the empty set

given $\{x:f(x)=\frac{1}{x}\}=?$
$f\left(x\right)=\frac{1}{2}\Rightarrow x-\left[x\right]=1.$
$x-\left[x\right]$ belongs to $[0,1]$
It is never 1, So. answer is c.