If A = {1, 2, 3}, B = {1, 2, 3}, why cannot f(x) = x² be called a function from A to B?

Correct answer: Because f(2) = 4, and 4 ∉ B.

For a mapping f: A → B to be a function, every element of A must be assigned exactly one value, and that value must belong to the codomain B. Although the rule x² gives a single value for each input, f(1)=1 and f(2)=4, while 4 is not an element of B={1,2,3}. Thus the mapping does not stay inside the declared codomain and cannot be a function from A to B. Option A identifies the first decisive failure. Option B is not a failure because 1 belongs to B, option C merely reports a value outside B without stating the correct input condition, and option D is irrelevant to the function requirement.