Given a function f and a subset A of its domain let f(A) represent the range of

Question

Given a function f and a subset A of its domain let f(A) represent the range of f over the set A; that is, f(A) = {f(x): x (element of) A}

Find two sets A and B for which f(A intesect B) does not equal f(A) intersect f(B).

Is the following correct? What should I do to make it clearer?

A=(-1,0) and B=(0,1). Then A intersect B = phi, so f(A intersect B) = f(phi)=phi. But since f(A) = f(B) = (0,1), f(A) intersect f(B) = (0,1). Therefore, f(A intersect B) "subset of not equal to" f(A) intersect f(B)

Explanation / Answer

You did not define the function f. With out defining it, we cannot conclude about f(A) and f(B).

Take the function to be f(x) =x^2, then your argument is totally perfect.

I have written it clearly on a paper and uploaded it at :   http://i.imgur.com/IJr9LPQ.jpg

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