If f(x) = x² and g(x) = 2, when will (f + g)(x) and (fg)(x) be equal?

Correct answer: x = ±√2

Use the definitions of addition and multiplication of functions. Since f(x) = x² and g(x) = 2, we have (f + g)(x) = x² + 2 and (fg)(x) = 2x². Set them equal: x² + 2 = 2x². Subtracting x² from both sides gives x² = 2, so the real solutions are x = √2 and x = −√2. Therefore option A is correct. Option B comes from confusing x² = 2 with x² = 4, option C does not satisfy the equation because 0 + 2 is not 0, and option D is false because two real solutions exist. Both functions are defined for every real x, so no additional domain restriction changes the answer.