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Supose that alpha lt x lt beta the solut...

Supose that `alpha lt x lt beta` the solution to the following inequality `((1)/(3))^(x^(2) + 1) gt ((1)/(9))^(x + 2)` then `beta - alpha` is equal to

A

`2`

B

`-2`

C

`5`

D

`4`

Text Solution

Verified by Experts

The correct Answer is:
D
`x^(2) + 1 lt 2x + 4 rArr x^(2) - 2x - 3 lt 0`
`(x - 3) (x +1) lt 0`
`-1 lt x lt 3`
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