Correct Answer - B
As `x^(2)-6x + 12 gt 0` for all x. Therefore, `"log"_(1//2)(x^(2)-6x + 12)` is defined for all` x in R`
Now,
`"log"_(1//2)(x^(2)-6x + 12) ge -2`
`rArr x^(2)-6x + 12 le ((1)/(2))^(-2)`
`rArr x^(2)-6x +8 le 0 rArr (x-2)(x-4) le 0 rArr x in [2, 4]`