Can anybody explain these two problems?

i know the answser for #1 is 6, but how do we solve it? Thank u ^^

- S = { (x, y) : |x| - |y| ≤ 1 and |y| ≤ 1 }, sketch the region S and find its area. (Putnam Test, A1, 1988)
- Consider a polynomial f(x) with real coefficients having the property f(g(x))=g(f(x)) for every polynomial g(x) with real coefficients. Determines and prove the nature of f(x). (Putnam competition)