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Greatest Integer Function

The solution ...

Question

The solution of the equation $2 x - 2 [x] = 1$ , where $[x]$ represents greatest integer function less than or equal to $x$ , are

x = n + \frac{1}{2}, n \in N

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x = n - \frac{1}{2}, n \in N

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x = n + \frac{1}{2}, n \in Z

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n < x < n + 1, n \in Z

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Solution

The correct option is B $x = n + \frac{1}{2}, n \in Z$
$2 x - 2 [x] = 1$
$\Rightarrow x - [x] = \frac{1}{2}$
$\Rightarrow {x} = \frac{1}{2}$ , where ${}$ is fractional part function
$∴ x = n + \frac{1}{2}, n \in Z$

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