In order for the square root to make sense, the argument (the terms inside the square root) should not be negative. (2x - 12)^1/2 is the square root of 2x - 12. Therefore, the inequality 2x–12 ≥ 0 should be satisfied. This means that x ≥ 6 must be satisfied. Hence, the largest domain of definition of f is [6, ∞).