The domain of y =\(\frac{1}{\sqrt{|x| -x}}\) is:(a) [0, ∞) (b) (0,

1.	The domain of y =\(\frac{1}{\sqrt{\|x\| -x}}\) is:(a) [0, ∞) (b) (0, ∞) (c) (– ∞, 0) (d) (– ∞, 0)
Answer» 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).

The domain of y =\(\frac{1}{\sqrt{|x| -x}}\) is:(a) [0, ∞) (b) (0, ∞) (c) (– ∞, 0) (d) (– ∞, 0)

Answer»

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).