Which option shows that two different inputs can have the same output in a function?

Correct answer: {(4,1),(5,1),(6,2)}

The governing concept is that a function assigns exactly one output to every input, but it may assign the same output to different inputs. Such a function is called many-one. In option A, input 4 maps to 1, input 5 also maps to 1, and input 6 maps to 2. Thus every listed input has exactly one image, while two distinct inputs share an output, so this is a valid function demonstrating the required situation. In option B, input 4 has two different outputs, 1 and 2, so it is not a function. Option C similarly gives input 5 two outputs. In option D, the stated domain element 5 has no image. Therefore A is correct.