1) If f(x) = x^2, where x is an element of real nos, and X is the characteristic function of [0,9], of what subset of R is X.f the characteristic function?
X is the the characteristic function of [0,9]. So
X(x) =1 if x is in [0,9]
X(x) =0 if x is not on [0,9]
X.f = X(f(x)) = X(x^2)
Now if B is a subset of R, whose characteristic function is X(x^2),
X(x^2) = 1 if (x^2) is in B,
X(x^2) = 0 if (x^2) is not in B.
Then how do i proceed. I don't know. I think the answer is either [0,3] or [0,81]. but i am not able to work it out.
2) Then immediately the successive question is :
If f: A--> B and Xe is the char. fn. of E which is a subset of B. Of what subset of A is Xe.f the char. fn.?
COuld you give me some hints on how to solve this one.