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Find the set of all real x for which the function f(x) = 3/(4 - x²) + log10(x³ - x) is defined.

1. (-1,0) ∪ (1,2) ∪ (2,∞)
2. (a,2)
3. (-1,0) ∪ (a,2)
4. (1,2) ∪ (2,∞)

Correct answer: (-1,0) ∪ (1,2) ∪ (2,∞)

Solution

The function f(x) is defined when the denominator of the rational part is non-zero and the argument of the logarithm is positive. The term 4 - x² must not equal zero, leading to x ≠ ±2, and x³ - x must be greater than zero, which is satisfied in the intervals (-1,0) and (1,2) ∪ (2,∞). Thus, the correct option includes all these intervals.

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