For each, find an appropriate function.

(a) Find a function $f(k)$ such that $$2 - 4 + 6 - 8 + 10 = \sum\limits_{k=1}^{5} f(k) .$$

$f(k)$ =

(b) Find a function $g(k)$ such that $$2 - 4 + 6 - 8 + 10 = \sum\limits_{k=0}^{4} g(k) .$$

$g(k)$ =