 # Algebra of Functions

## A set of all rational and irrational numbers is called real numbers, and it is denoted by R. A relation f from a non-empty set A to a non-empty set B is said to be a function, if:(i) an element of set A is associated to a unique element in set B. (ii) all the elements of set A are associated to the elements of set B. The set of all the real numbers for which a real valued function is defined is called the domain of that function.If f and g are two real valued functions with domains A and B respectively then their sum, difference, product and quotient are defined as follows:(f + g)(x) = f(x) + g(x), for all x ? A ? B(f – g)(x) = f(x) – g(x), for all x ? A ? B(f.g)(x) = f(x)g(x), for all x ? A ? B(f/g)(x) =f(x)/g(x), provided g(x) ? 0, x ? A ? BThe product (? f) is a real function and defined by (? f)(x) = ? f(x), x ? A.Where, f be a real function with domain A and ? be a scalar.Keywords: Multiplication by a Scalar.

To Access the full content, Please Purchase

• Q1 Marks:5   • Q2 Marks:5    • Q3 Marks:3 • Q4 Marks:3    