Hello wonderful mathematics people, this is Anna Cox from Kellogg Community College combining functions if we have two separate functions f and g, we can add the two functions so the quantity f plus g of x equal f(x) plus g(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 zero 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 should be functions are defined things to remember: we cannot divide by zero or have a negative under and even radical root for a real number, so I could not have the square root of negative four, say or the fourth root of negative 81 those are not possibilities for a real domain composite function is a function within function. So we put g(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