They don’t have any more information available than when receiving 1 input, so they actually have to give the same outputs as one of the functions that takes only 1 input. There are only 4 binary functions of 1 input: one, zero, not, identity which correspond to the 4 possible truth tables for a function with 1 input (10, 11, 00, 01 are the only 4 options). (The one and zero functions don’t actually need any input because the output is the same regardless of the input.)
Make sense?