Question

If $f:R\to R$ is defined by $f\left(x\right)=x-\left[x\right]+\frac{1}{4},$ where $\left[x\right]$ is the greaterst integer not exceeding $x$, then the set $\{x\in R:f(x)=\frac{1}{4}\}$ is equal to

• A. $N$, the set of all natural numbers
• B. $W$, the set of all whole numbers
• C. $Z$, the set of all integers
• D. $Q$, the set of all rational numbers

Answer 1

The correct option is C $Z$, the set of all integers

$x-\left[x\right]+\frac{1}{4}=\frac{1}{4}$
$x=\left[x\right]$
$\Rightarrow x$ is an integer.