# Easy question about linear transformation

• Nov 16th 2011, 01:24 PM
expresstrain
Hi,

(T(f))(t) = f(-t) (t is from -pi to pi.)

Show that T is linear.
• Nov 16th 2011, 01:35 PM
TheEmptySet
Re: Easy question about linear transformation
Quote:

Originally Posted by expresstrain
Hi,

(T(f))(t) = f(-t) (t is from -pi to pi.)

Show that T is linear.

Just use the defintion of linearity!

A map T is linear if for any scalars $a,b$ and any vectors $f,g$ we have

1. $T(af+bg)=aT(f)+bT(g)$

try this and post back if you get stuck.