If I < x < I +1 , find [-x] where I is an integer.

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Solution

[x] is the greatest integer function

If I < x < I +1 means x is between I and I +1.

$\Rightarrow$ - I -1 < -x < - I , -x lies between (- I-1) and - I

$\Rightarrow$ [-x] = - I - 1

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If I < x < I +1 , find [-x] where I is an integer.

[x] is the greatest integer function If I < x < I +1 means x is between I and I +1. ⇒ - I -1 < -x < - I , -x lies between (- I-1) and - I ⇒ [-x] = - I - 1

[x] is the greatest integer function

If I < x < I +1 means x is between I and I +1.

$\Rightarrow$ - I -1 < -x < - I , -x lies between (- I-1) and - I

$\Rightarrow$ [-x] = - I - 1