If graph of a function `f(x)` which is defined in [-1, 4] is shown in the following figure then identify the correct statement(s).

Options

A. domain of `f(|x|-1) " is " [-5,5]`
B. range of `f(|x|+1) " is " [0, 2]`
C. range of `f(-|x|) " is " [-1, 0]`
D. domain of `f(|x|) " is " [-3,3]`

Answer

A, B, C

Explanation

(1) `-1 le |x| -1 le 4`
`implies 0 le |x| le 5 implies -5 le x le 5`
(2) `f(|x|+1)`
range of `f(|x|+1)` is [0, 2]

(3) range of `f(-|x|) ` is [-1, 0]

(4) `-1 le |x| le 4`
`implies x in [-4,4]`