3. Prove that if A and B are sets then:

3. Let f(x) = x^2 + 1 and g(x) = x + 2. Find the composite function?
   f ° g.

Hi, math01-ga:

Let me address the question about composition of functions.  The other
part is perhaps incomplete?

The answer would depend on whether your are American or European, at
least in your mathematical outlook.

American mathematicians prefer to interpret f ° g to mean, first "do"
g and then apply f to the result:

f ° g (x) = f(g(x)) = (x+2)^2 + 1 = x^2 + 4x + 5

but British and Continental mathematicians reverse the order of
application to mean, "do" f followed by g:

f ° g (x) = g(f(x)) = (x^2 + 1) + 2 = x^2 + 3

Note that the answers are different, depending on the interpretation.

Both interpretations have their attractions.  The "American" approach
seems natural if you look at the functional notation which flows from
it, but the other interpretation is consistent with how permutation
calculations are done on both sides of "the pond".

regards, mathtalk-ga

f o g(x) = x^2 + 4x + 5

Prove:
f o g(x) = f(g(x))
f(g(x)) = (x+2)^2 + 1
= x^2 + 4x + 4 + 1
= x^2 + 4x + 5

I'm sorry replace all those 1's with 2's. the final answer is x^2 + 4x + 6