What is the value of [x] + [-x] , where [x] is the greatest integer function

-1

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Solution

The correct options are
A
-1

B
0

[x] is the greatest integer function. We know [2.1] = 2. Consider 1-2.11. It is equal to -3. We can write it as

-2-1 = -[2.1]-1.

=> [2.1] = -[2.1]-1. That is when x is not an integer, [-x] = -[x] - 1. Similarly, if we consider [-x], when x is an integer,

we get it as - [x] (You can consider more integers and check if this condition applies).

So we can conclude it as
.[x] + [—x] = —1 if x is not a integer
if
0 if is an integer
x is an integer is not an integer
$[- x] = {\begin{matrix} - [x], & i f x i s a n i n t e g e r - 1 - [x], & i f i s n o t a n i n t e g e r \end{matrix}$

$\Rightarrow [x] + [- x] = {\begin{matrix} 0, & i f i s a n i n t e g e r - 1, & i f x i s n o t a n i n t e g e r \end{matrix}$

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