Final answer:
The value x = 4 is the correct choice which is option c to ensure the relation A becomes a function, as it does not duplicate any first element already present in the set A.
Step-by-step explanation:
The student has asked which value for x will make the relation A a function. A relation is considered a function if every input (x-value) is associated with exactly one output (y-value). Looking at the given set A = {(5,2), (7,4), (9,10), (x,5)}, we should pick a value for x that has not already appeared as a first element in any other pair in A. The values 5, 7, and 9 are already taken as first elements.
The only option not already used as a first element is C. 4. Therefore, choosing x = 4 will ensure that every x-value is associated with one unique y-value, thereby making the relation a function. Picking any of the other options would result in a repeated x-value, which would mean the relation is not a function.