Question

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

• A. -1
• B. 0
• C. 1
• D. 2

Answer 1

Answer: (A), (B)

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
$[-x]=\{\begin{array}{cc}-\left[x\right],& ifxisaninteger\\ -1-\left[x\right],& ifisnotaninteger\end{array}$

$\Rightarrow \left[x\right]+[-x]=\{\begin{array}{cc}0,& ifisaninteger\\ -1,& ifxisnotaninteger\end{array}$