We want to fill in the blanks in the following statement.
Two functions f and g can be combined by the arithmetic operations of , , , and to create new functions.
Similar to how two real numbers can be combined by the operations of addition, subtraction, multiplication, and division to form other real numbers, two functions can be combined to create new functions. Let f and g be two functions with overlapping domains. Then, for all x common to both domains, the four operations of f and g are defined as in the following table.
Addition
(f+g)(x)=f(x)+g(x)
Subtraction
(f-g)(x)=f(x)-g(x)
Multiplication
(fg)(x)=f(x)* g(x)
Division
(f/g)(x)=f(x)/g(x), g(x)≠0
We can now fill in the blanks in the given statement.
Two functions f and g can be combined by the arithmetic operations of addition, subtraction, multiplication, and division to create new functions.
