Question

how do you know if a function is legitimate i know that it need to have only one of y into each x but is there anything else like proof?

Answer 1

@Michele_Laino

Answer 2

by definition,
"a function f is a relationship between two variables, namely x, y:
\[f:x \rightarrow y=f(x)\]
such that for every x beloging to the domain of f, there exist an unique y belonging to the range of f"