# Combining functions and determining domain

When you find a composition of a functions, combining functions and determining domain is no longer x that is being plugged into the outer function, it is the inner function evaluated at x. Self Combining functions and determining domain Problem 7. While the arithmetic combinations of functions are straightforward and fairly easy, there is another type of combination called a composition. For multiple combinations, follow the order of operations by performing multiplication and division before addition and subtraction. The domain of the difference is also the intersection of the domain of f with the domain of g.

The domain of the composition is the portion of the domain of g whose image under g lies within the domain of f. For multiple combinations, follow the order of operations by performing multiplication and division before addition and subtraction. Self Check Problem 4.

It's much better than having a factor of h in the denominator because in calculus, we're going to let h approach 0 and we'll want to just plug a zero combining functions and determining domain for h. The domain of the difference is also the intersection of the domain of f with the domain of g. For data presented in a table, compute combinations the same way, simply add, subtract, multiply, divide, or perform a composition.

State the domain of the new function. The range of the sum is impossible to predict, since f might be at its highest while g is at its lowest, or g might be just a multiple of combining functions and determining domain. The domain and range are both all real numbers. It has been easy so far, but now we must consider the Domains of the functions. The domain of the product is the intersection of the domain of f with the domain of gas well.

The order is important. Then, write g x in the brackets and simplify. I can't do that symbol in text mode on the web, so I'll use a lower case oh " o " to represent composition of functions.

Self Check Problem 2. What if we reverse the order of f and g? Recall that the domain is the set of all x -values and the range is the set combining functions and determining domain all y -values. Shown below is the graph of f in greenthe graph of g in red and the graph of f g in pink. Self Check Problem 5.