# Simple Question about showing convex:

• Sep 7th 2009, 09:38 AM
sunnysky777
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
• Sep 7th 2009, 10:43 AM
Plato
Quote:

Originally Posted by sunnysky777
Show that the following function, having domain {0.1. ...., n -1 }, is convex:

f(j) = 1/ (n-j).

How does the textbook define convex functions?
• Sep 7th 2009, 11:02 AM
sunnysky777
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:)
• Sep 7th 2009, 11:41 AM
Plato
Quote:

Originally Posted by sunnysky777
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).

Well then apply that definition to the function $\displaystyle f(j)=\frac{1}{n-j}$ where $\displaystyle j\in \{0,1,...,n-1\}$.