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

Options

A. A. `[-1,2)`
B. B. `[1,2]`
C. C. `[-1,1]`
D. D. `[0,3sqrt(4))`

Answer

A

Explanation

`(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)`