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Since you can't take the square root of a negative number, the expression under the square root must be equal to, or greater than, zero. Just solve this inequality, with the expression under the square root.

If I understand correctly, the expression under the root is 9x2-4. For the inequality, get the critical points through an equation first: 9x2-4 = 0; 9x2 = 4; x2 = 4/9; x = plus-or-minus 2/3. Analyzing any points to the left of -2/3, between -2/3 and 2/3, and to the right of 2/3, you quickly see that the inequality is fulfilled for any number that is either <= -2/3, or >= 2/3.

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Q: What is the domain of f of x equals the square root of 9x the power of 2 - 4?
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