Question

For f to be a function, what is the domain of f, if f(x) = 1/√(|x| - x)?

a. (-∞, 0)

b. (0, ∞)

c. (-∞, ∞)

d. (-∞, 0]

Answer 1

Correct option a. (-∞, 0)

Explanation:

f(x) is defined if 

|x| – x > 0 ⇒ |x| > x 

For x > 0, x > x, (not possible) 

For x < 0, –x > x ⇒ 2x < 0 

⇒ x < 0 (possible) 

So, domain of f = (-∞, 0)