Question

find the domain of x/( |x-2|-3)

Answer 1

Answer:

x < -1 (or) -1 < x < 5 (or) x > 5

Step-by-step explanation:

Given: x/(|x - 2| - 3)

⇒ |x - 2| - 3 = 0

⇒ |x - 2| = 3

(i)

x - 2 = -3

x = -3 + 2

x = -1

(ii)

x - 2 = 3

x = 3 + 2

x = 5.

Hence, x = -1,5.

Therefore:

Function Domain: x < -1 or -1 < x < 5 or x > 5

Interval Notation: (-∞,-1) ∪ (-1,5) ∪ (5,∞).

Hope it helps!