In Computer Programming: Meryn Stol voted up this answer. Robert J. Kolker Suppose a function f returned two values for x,  say v1 and v2.  If you substitute f(x) in another expression to get a result  which value did you substite? v1 or v2? The ambiguity makes a conclusion impossible.  So a function has to return exactly  one value from its co-domain. See question on Quora - Meryn Stol