The volume of a cube with edge length e is modeled by the function v(e)=e3. find a function for the edge of a cube given its volume.

V(e) = e^3.

For any value of e, (the edge length), just cube it to get the volume. Easy

V(-2) = -8
V(-1) = -1
V(0) = 0
V(1) = 1
V(2) = 8
V(3) would be 27...etc

It doesn't make sense to use a negative or zero value for e (since you can't have a length like that), so technically there should be a restriction of e > 0.

To find the edge length given the volume, we would just solve for e.

V = e³
Take the cube root of each side...
∛V = ∛e³
∛V = e

Write as e(V) = ∛V.