1.

The set of real values of x satisfying `"log"_(0.2) ((x+2)/(x)) le 1`, isA. `(-oo, -5//2] cup (0, oo)`B. `[5//2, oo)`C. `(-oo, -2) cup (0, oo)`D. none of these

Answer» Correct Answer - A
Note that `"log"_(0.2) ((x+2)/(x))` is meaningful, if
`(x+2)/(x) gt0 rArr x in (-oo, -2) cup (0, oo)`
Now,
`"log"_(0.2) ((x+2)/(x)) le 1`
`rArr (x+2)/(x) ge (0.2)^(-1)`
`rArr (x+2)/(x) ge (1)/(5)`
`rArr (x+2)/(x) - (1)/(5) ge 0`
`rArr (4x + 10)/(5x) ge 0 rArr (2x+5)/(x) ge 0 rArr x in (-oo, -5//2] cup (0, oo)`


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