Proving Convexity of g with f's Convexity

[ahamdiheme]

Homework Statement

Let f:Rⁿ$$\rightarrow$$R^nxmtex] and b$$\in$$Rⁿ. Define g:R^m$$\rightarrow$$R by
g=f(Ax+b)
Show that g is convex if f is convex

Homework Equations

The Attempt at a Solution

I need hints on how to go about this please.

 

[Unco]

Hi ahamdiheme,

What is the definition of a convex function? Immediately from that you should realize that f must be real-valued in order to be convex; also, I assume A is an nxm matrix.

To get the manipulation right in the inequality (when you look to apply the definition), it will help to write down what you want to arrive at to make the manipulation easier.

Show your work if you get stuck.