For any real number $x, & k$ is an integer, if $k < x < k + 1,$ then $[- x] =$

- k

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- k + 1

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- k - 1

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Solution

The correct option is C $- k - 1$
Given: $x$ to be any real number and $k$ be any integer.
Also, $k < x < k + 1$
To find: $[- x]$
Multiplying each side of the inequality $k < x < k + 1$ by $- 1$ , we get:
$- k > - x > - k - 1$
$Or - k - 1 < - x < - k$
$\Rightarrow x$ will lie between the interval $(- k - 1, - k)$
$\Rightarrow [- x] = - k - 1$

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