I have a affine transformation:

f(x)=Ax+a where A is a 2x2 martix x and a are vectors

and I also have the function

g(x)=Bx + b where B is a 2x2 martix x is a vector

how would I go about combining them (ie g o f) as in forming a composite would it be like this :

Thanks in advance for any help.