Given:

≥ 0, x ϵ R. – {–2, 2}

Intervals of |x|:

x ≥ 0, |x| = x and x < 0, |x| = -x

Domain of ≥ 0

is not defined for x = -2 and x = 2

Therefore, Domain: x < -2 or -2 < x < 2 or x > 2

Combining intervals with domain:

x<-2, -2<x<0, 0 ≤ x<2, x>2

For x < -2:

≥ 0

Signs of – x – 1:

-x -1 = 0 → x = -1

(Adding 1 to both the sides and then dividing by -1 on both the sides)

-x – 1> 0 → x < -1

(Adding 1 to both the sides and then multiplying by -1 on both the sides)

-x – 1 < 0 → x > -1

(Adding 1 to both the sides and then multiplying by -1 on both the sides)

Signs of – x – 2:

-x -2 = 0 → x = -2

(Adding 2 to both the sides and then dividing by -1 on both the sides)

-x – 2> 0 → x < -2

(Adding 2 to both the sides and then multiplying by -1 on both the sides)

-x – 2 < 0 → x > -2

(Adding 2 to both the sides and then multiplying by -1 on both the sides)

Intervals satisfying the required condition: ≥ 0

x < - 2 or x = -1 or x > -1

Merging overlapping intervals:

x < -2 or x ≥ -1

Combining the intervals:

x < -2 or x ≥ -1 and x < -2

Merging overlapping intervals:

x < -2

Similarly, for -2 < x < 0:

≥ 0

Therefore,

Intervals satisfying the required condition: ≥ 0

x < - 2 or x = -1 or x > -1

Merging overlapping intervals:

x < -2 or x ≥ -1

Combining the intervals:

x < -2 or x ≥ -1 and -2 < x < 0

Merging overlapping intervals:

-1 ≤ x < 0

For 0 ≤ x < 2,

≥ 0

Signs of x – 1:

x – 1 = 0 → x = 1(Adding 1 to both the sides)

x – 1 > 0 → x > 1(Adding 1 to both the sides)

x – 1 < 0 → x < 1(Adding 1 to both the sides)

Signs of x – 2:

x – 2 = 0 → x = 2(Adding 2 to both the sides)

x – 2 < 0 → x < 2(Adding 2 to both the sides)

x – 2 > 0 → x > 2(Adding 2 to both the sides)

At x = 2, is not defined

Intervals satisfying the required condition: ≥ 0

x < 1 or x = 1 or x > 2

Merging overlapping intervals:

x ≤ 1 or x > 2

Combining the intervals:

x ≤ 1 or x > 2 and 0 ≤ x < 2

Merging overlapping intervals:

0 ≤ x ≤ 1

Similarly, for x > 2:

≥ 0

Therefore,

Intervals satisfying the required condition: ≥ 0

x < 1 or x = 1 or x > 2

Merging overlapping intervals:

x ≤ 1 or x > 2

Combining the intervals:

x ≤ 1 or x > 2 and x > 2

Merging overlapping intervals:

x > 2

Combining all the intervals:

x < -2 or -1 ≤ x < 0 or 0 ≤ x ≤ 1 or x >2

Merging the overlapping intervals:

x < -2 or -1 ≤ x ≤ 1 or x > 2

Therefore,

x ϵ (-∞, -2) Ս [-1,1] Ս (2, ∞)