What is the domain of the function f(x) = 1 / (|x| - x)?

Model Answer & Options

Source: Extra Practice

(-∞, 0)

(0, ∞)

R - {0}

Empty set

Explanation

For the function to be defined, the denominator |x| - x must not be zero. |x| - x = 0 occurs when |x| = x, which is true for all x ≥ 0. Therefore, x cannot be zero or any positive number. However, for x < 0, |x| = -x, so the denominator becomes -x - x = -2x, which is positive and non-zero. Thus, the domain is all negative real numbers, (-∞, 0). Option B and C include values where the denominator becomes zero.

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