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If |(12x)/(4x^(2)+9)| le 1, then (a) x ...

If `|(12x)/(4x^(2)+9)| le 1`, then (a) `x in R` (b) `x in [-3,3]` (c) `x in [-1,oo)` (d) `x in (-oo,2]`

A

`x in R`

B

`x in [-3,3]`

C

`x in [-1,oo)`

D

`x in (-oo,2]`

Text Solution

Verified by Experts

The correct Answer is:
A
`(a)` `|(12x)/(4x^(2)+9)| le 1`
`-1 le (12x)/(4x^(2)+9) le 1`
Since `4x^(2)+(9)` is postive for all real `x`, we can multiply by `4x^(2)+9`
`:. -(4x^(2)+(9)) le 12x le (4x^(2)+(9))`
`(2x+3)^(2) ge 0` and `(2x-3)^(2) ge 0`
Above is true for all real values of `x`.
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