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The solution of the inequality (|x+2|-|x...

The solution of the inequality `(|x+2|-|x|)/(sqrt(8-x^(3))) ge 0` is

A

`[-1,2]`

B

`[1,2]`

C

`[-1,1]`

D

`[0,3sqrt(4))`

Text Solution

Verified by Experts

The correct Answer is:
A
`(a)` `(|x+2|-|x|)/(sqrt(8-x^(3))) ge 0`
We must have `8-x^(3) gt 0`
`implies x^(3) lt 8 implies x lt 2`
Also `|x+2|-|x| ge 0`
`implies |x+2| ge |x|implies (x+2)^(2)-x^(2) ge 0 implies 2(x+1) ge 0`
`implies x ge -1`
So `x in [-1,2)`
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