Hi (excuse me about my english).

I have a doubt about this linear transformation: f(x) = x - 1

There is a theorem that says that if the kernel of the transformation is 0; then the transformation is inyective:

if the ker (f(x)) = 0

But in this linear transformation the ker (f) = { x = 1 } ; because 1 - 1 = 0

So the transformation could not be linear, what am I doing wrong?.

Thank you in advance