SOLUTION: how do i know if f(x)= x/6 is a function. if it is how do i explain it?

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Question 765689: how do i know if f(x)= x/6 is a function.
if it is how do i explain it?

Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
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) = x%2F6

Solve y = x%2F6 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