# Convex Function

#### ahamdiheme

How do i go about showing that if f(x)=$$\left\|$$x$$\left\|$$ then f(x) is a convex function.

I'm thinking in the direction of the triangle inequality but don't know how to go about it. Any clues? thanks

#### tim_lou

it just comes straight from definition of convex function

$$|tx+(1-t)y|\leq |tx| + |(1-t)y|$$

#### ahamdiheme

that is it, Thanks a lot!

Last edited:

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