If A={1,2,3} and f(x)=x²+1, to which codomain can f be considered a function from A?

Correct answer: {2,5,10}

For a function f:A→B, every input in the domain A must have exactly one output, and every output must belong to the stated codomain B. Evaluate the rule on all elements of A: f(1)=1²+1=2, f(2)=2²+1=5, and f(3)=3²+1=10. Therefore the image set is {2,5,10}. This set can serve as the codomain, so option A is correct. The set {1,4,9} contains the squares before adding 1, not the actual outputs. The set {2,4,6} misses 5 and 10, while {1,2,3} does not contain all outputs. A larger codomain could also work mathematically, but among the given choices only option A contains exactly the required images.