Hello wonderful mathematics people. This is Anna Cox from Kellogg Community College combining functions. If we have two separate functions F&G, we can add the two functions so the quantity F + g of X equal F of X + g of X. We could also subtract the two functions, multiply the two functions, and divide the two functions. If you divide the two functions, you need to be careful that the G of X function or whichever one you have on the bottom can never equal 0. Now we need to refer to and talk about domains, because as we start combining functions, we have to actually look at the overall domain of the combination in addition to each individual domain. So the domain of all real values where the function is defined, actually it probably should be. Functions are defined things to remember. We cannot divide by zero or have a negative under an even radical root for a real number. So I could not have sqrt -4, say, or the 4th root of -81. Those are not possibilities for a real domain. Composite function is a function within a function. So we put G of X into our F equation and this is the domain as the set of all X where X is in the domain of G. So this X had to be in the domain of G and then the G of X has to all be within the domain of F. Thank you and have a wonderful day.