You missed smth over here:
(a + b*)* =

Correct the problem and we'll try to help.

this is a question at the defined functions

I'm sorry, I'm not familiar with it... I'm not from the US and you guys might have slightly different notations... If you would be so kind as to explain, maybe I could help...

Is there another piece of important information that goes along with this problem? If not, then I don't think this problem is solvable.

I found the answer in the book, but don't understand it really :$

(a + b*)* = (a + [2 – b])* = (a + 2 – b)* = 2 – (a + 2 – b) = 2 – a – 2 + b = –a + b = b – a. The answer is
(A).

The problem might be wrong, but with the info that you provided I believe that the "*" operation is defined as:
x* = 2 - x.
After defining the problem, they ask you to calculate (a + b*)*. You begin by working the stuff in the parenthesis: b* = 2 - b and you replace b* in the initial form:
(a + b*)* = (a + 2 - b)*.
Now, from this point you consider a + 2 - b as a number on its own and you apply the operation:
(a + 2 - b)* = 2 - (a + 2 - b) = 2 - a - 2 + b = b - a.

Deepoe, please check the question again. How come one put b=2-b fomr nowhere... there should a defined function as DanaJ said.