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

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 term 3/(4-x^2) requires x != +/-2, and log10(x^3-x) requires x^3-x = x(x-1)(x+1) > 0, i.e. x in (-1,0) U (1,inf). Removing x = 2 gives the domain (-1,0) U (1,2) U (2,inf).

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