1.

2. Can you please explain the last 2 lines ( how he got lg(2^k)*2??? )

Show that if f (n) and g(n) are monotonically increasing functions, then so are the functions fin)+g(n) and f(g(n), and if f (n) and g(n) are in addition nonnegative, then f(n).g(n) is monotonically increasing