Recent content by mathcrazy

What is f(g(x))? f(x)= sqrt(x) g(x)= x^2 am i crazy or is this not x??? In the back of my book, it says that this is not x. I thought it might have to do with the range of g not being in the domain of f....but the range of g is in the domain of f!!! also, f(x)=sin(x) g(x)=inverse sin(x)...

What is f(g(x))? f(x)= sqrt(x) g(x)= x^2 am i crazy or is this not x??? In the back of my book, it says that this is not x. I thought it might have to do with the range of g not being in the domain of f....but the range of g is in the domain of f!!! also, f(x)=sin(x) g(x)=inverse sin(x)...

a. How can I prove that the intersection of two countable sets is countable? hint: there is a very short answer and b. prove whether or not the intersection and union of two uncountable sets must be uncountable. How do i even begin the second? best answer will definitely be voted!

let's see who's smart enough out there to prove these :) -(a-b) = -a +b and (a-b)+(b-c) = a - c best answer will be voted ;-)