# Math Help - Simple Question about showing convex:

1. ## Simple Question about showing convex:

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

2. 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?

3. 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

4. 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 $f(j)=\frac{1}{n-j}$ where $j\in \{0,1,...,n-1\}$.