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