Originally Posted by

**poorna** 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),

then,

**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 **X**e is the char. fn. of E which is a subset of B. Of what subset of A is **X**e.f the char. fn.?

COuld you give me some hints on how to solve this one.