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If [log2(x/([x]))]geq0, where [.] denote...

If `[log_2(x/([x]))]geq0,` where [.] denote the greatest integer function, then

A

`x in (-oo, oo) ~[0, 1)`

B

`x in ( -oo, 0)`

C

`x in [ 1, oo)`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
`["log"(x)/([x])] ge 0`
`rArr log_(2) ((x)/([x])) ge 0 rArr (x)/([x]) ge 1`
`rArr (x-[x])/([x]) ge 0 rArr ({x})/([x]) ge 0`
It implies that .x. is any positive real number greater than or equal to one or x is any non-zero integer.
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