Page 106 - DMTH401_REAL ANALYSIS

Real Analysis Sachin Kaushal, Lovely Professional University

Notes Unit 9: Functions

CONTENTS
Objectives
Introduction
9.1 Algebraic Functions
9.1.1 Algebraic Combinations of Functions

9.1.2 Notion of an Algebraic Function
9.2 Transcendental Functions
9.2.1 Trigonometric Functions
9.3 Inverse Trigonometric Functions
9.3.1 Monotonic Functions
9.3.2 Logarithmic Function
9.3.3 Exponential Function

9.4 Some Special Functions
9.4.1 Identity Function
9.4.2 Periodic Function
9.4.3 Modulus Function
9.4.4 Signum Function
9.4.5 Greatest Integer Function
9.4.6 Even and Odd Functions
9.4.7 Bounded Functions
9.5 Summary

9.6 Keywords
9.7 Review Questions
9.8 Further Readings

Objectives

After studying this unit, you will be able to:
 Discuss the different types of algebraic functions
 Explain the trigonometric and the inverse trigonometric functions

 Describe the exponential and logarithmic functions
 Explain some special functions including thus bounded and monotonic functions
Introduction

Real Analysis is often referred to as the Theory of Real Functions. The word 'function' was first
introduced in 1694 by L.G. Leibniz [1646-1716], a famous German mathematician, who is also

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