In which option does each element of A = {3,6} have exactly one image?

Correct answer: {(3,9),(6,12)}

The governing concept is the defining test for a function from a domain: every domain element must occur as a first component exactly once, with one associated output. In option A, the domain elements 3 and 6 each appear once, paired with 9 and 12 respectively. Therefore it satisfies the stated condition. In option B, 3 has two images and 6 has none. In option C, 3 has no image, so the relation is incomplete for the domain A. In option D, 6 has two different images, 12 and 9, while 3 has one. Thus only option A gives every element of A exactly one image, irrespective of whether different domain elements might share an output in other examples.