Halp

How do I proved this?

Assume h : R -> R is continuous on R. Let K = {x : h(x)=0}. Show that K is a closed set.

Riddle me this, guys.

There exists 0 < c < 1 such that abs( f(x) - f(y) ) < c * abs(x-y).
Let y_n be the sequence (y_1, f(y_1), f(f(y_1)), ...).
Show that y_n is a Cauchy sequence first. Let y = lim y_n. Then show y = f(y) and that y is unique. And then show x_n = (x, f(x), f(f(x)), ...) converges to y using definition y = lim y_n.