For contradiction we assume f(x) is NOT a function.
Then there must be two different outputs for the same input,
Let a be the input and b and c be the two different outputs, b ≠ c.
Then (a,b) and (a,c) are both elements of the relation where b ≠ c.
Let y = f(x) =
Solve y =
for x
6y = x
Substitute (a,b) and (a,c)
6b = a, 6c = a
then 6b = 6c
b = c.
That contracts the assumption that b ≠ c
Therefore the assumption that f(x) is not a function
is false, and therefore f(x) is a function.
Edwin