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Definition 3

The absolute value | a | of a Î R is defined to be equal to . Thus = | a |

For example (i) If a = -2 then = | - 2 | = 2

(ii) If a = 0 then = | 0 | = 0

We have some simple but important results

1 ® | a - b | = | b - a |

2 ® - | a | £ a £ | a |

3 ® | a . b | = | a | . | b |

4 ®

5 ® | a + b | £ | a | + | b |

6 ® | a - b | > | a | - | b |

7 ® | a + b | > | a | - | b |


Example 1 Solve the inequality x + 3 < 7 x Î N

Solution :

x + 3 < 7 .. ( subtracting 3 from both sides)

   x + 3 - 3 < 7 - 3
x < 4

Example 2 Solve and graph 3 £ < 5

Solution :

Breaking 3 £ < 5 into two inequalities as

3 £ and < 5

9 £ 2x - 1 and 2x - 1 < 15

9 + 1 £ 2x - 1 + 1 and 2x - 1 + 1 < 15 + 1

10 £ 2x and 2x < 16

£ and <

Thus the solution set is 5 £ x < 8 or [5, 8)

Graph :

 

 

Index

Introduction

1.1 Functions And Mapping
1.2 Functions, Their Graphs and Classification
1.3 Rules for Drawing the Graph of a Curve
1.4 Classification of Functions
1.5 Standard Forms for the equation of a straight line
1.6 Circular Function and Trigonometry

Chapter 2





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