For the graph of (f(x)=min(x^2,4)), what is (f(x)) when (|x|≥2)?

Correct answer: 4

The governing concept is the minimum operator together with the implication of the condition |x|≥2. Both |x| and 2 are non-negative, so squaring preserves the inequality and gives x²≥4. The function f(x)=min(x²,4) chooses the smaller of x² and 4. Since x² is at least 4 throughout the stated region, the smaller value is always 4. Equality occurs at |x|=2, and for larger absolute values x² is even greater, so the conclusion remains unchanged. Therefore option A is correct. Option B would apply where x²≤4, namely |x|≤2, while 2 and 0 are not selected by the minimum expression under the given condition.