The domain of y = 1 / √{|x|-x} is:

Question

The domain of y =\(\frac{1}{\sqrt{|x| -x}}\) is:

(a) [0, ∞) 

(b) (0, ∞) 

(c) (– ∞, 0) 

(d) (– ∞, 0)

Answer 1

Answer : (c) (– ∞, 0) 

For the function y = \(\frac{1}{\sqrt{|x|-x}} \)  to be defined,

| x | – x > 0 as | x | – x ≠ 0 

⇒ | x | > x which is only possible when x < 0 as | x | = x for all x ≥ 0.

∴  Domain of y = \(\frac{1}{\sqrt{|x|-x}} \)  is x < 0 or (– ∞, 0).