# Thread: [SOLVED] fog is a linear transformation, is f and g?

1. ## [SOLVED] fog is a linear transformation, is f and g?

Hello,

I'm struggling trying to see if f and g are linear transformation when fog is a linear transformation.

fog a linear transformation =>? f and g are linear transformations

Let's say g
(x,y) |-> (x+2,y)

and f
(x,y) |-> (x-2,y)

fog will be a linear transformation but not f and g... right?
I'm not sure to have the correct definition of what is linear.

Thanks (:

2. An application is said to be linear if $f( \alpha x + \beta y ) = \alpha f(x) + \beta f(y)$

3. Allright, so it's correct.