
Sets

Relations and Functions

Trigonometry

Principle of Mathematical Induction

Complex Numbers

Quadratic Equations

Permutations and Combinations

Binomial Theorem

Sequence and Series

Straight Lines

Circles

Limits and Derivatives

Statistics

Probability

Conic Section

Introduction to ThreeDimensional Geometry

Mathematical Reasoning

Correlation Analysis

Index Numbers and Moving Averages
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 nonempty set A to a nonempty 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 ? B
The 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.
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