Show that the following function, having domain {0.1. ...., n -1 }, is convex:
f(j) = 1/ (n-j).
I don't understand how to deal with the domain part and what it means, I am very new to discrete math...please help me and explain...Thank you
Definition:
Let f be a function whose domain is the set of integers, and define the function g by
g (i) = f(i) - f(i-1))
we say that f is a convex function if g is an increaseing fuction; that is, f is convex if for all i,
f(i+1) - f (i) > or = f(i) -f (i-1).
Thank you