too late, I am already in the middle of semester.
we need to find an x so that f(x) = c, for any c we choose. so x should be "some expression (formula) in c".
what is f(x)? by the definition:
. so if f(x) = c, we have:
. now, we need to try to "solve for x".
(adding 4 to both sides)
(dividing both sides by 2)
(taking the cube root of both sides). this is the x we are looking for (we hope).
to check, we verify that f(x) is indeed c, when .
,
so we indeed found an x that f sends to c.