Victor will start paying off his credit card in January. He uses the function f(x)=-35x+2,500 to model the amount of money he owes x months after January. How much money does he owe at the beginning of January?

To find out how much money Victor owes at the beginning of January, we need to substitute x = 0 into the function f(x)=-35x+2,500.

f(0) = -35(0) + 2,500 = 0 + 2,500 = 2,500.

Therefore, Victor owes $2,500 at the beginning of January. Answer: \boxed{2,500}.