The domain of the function is,
The domain of the function is,
Answer: D. (-∞,0) — Answer: (-∞,0) Requirement for the domain: the denominator sqrt(|x|-x) must be defined and not zero, so we need |x|-x > 0. If x ≥ 0, then |x| = x, so |x| - x…
- A.
-∞,∞-{0}
- B.
-∞,∞
- C.
(0,∞)
- D.
(-∞,0)
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Correct answer: D
Answer: (-∞,0)
Requirement for the domain: the denominator sqrt(|x|-x) must be defined and not zero, so we need |x|-x > 0.
If x ≥ 0, then |x| = x, so |x| - x = 0. This makes the denominator zero, so these x are not allowed.
If x < 0, then |x| = -x, so |x| - x = -x - x = -2x. For x < 0 this is positive, so the square root is defined and nonzero.
Therefore the domain is all real x with x < 0, i.e. (-∞,0).
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