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Example 6 Find the mistake from the following solution.

Suppose

Þ x - 3 £ 2 ....[Canceling - x2 - 5 from the denominator]

Þ x £ 5

Solution :

If a < b and c < 0,    then ac > bc .....(I)

Since (- x2 - 5) < 0 then

(- x2 - 5) (-x2 - 5) Þ x - 3 2 ....(by I)

Þ x - 3 + 3 2 + 3 \ x 5

Example 7 Show that the following in equality is consistent
(3x + 15) > x + 5

Solution :

(3x + 15) > x + 5

Þ x + 5 > x + 5

The inequality is consistent

Example 8 If x + y > 0 and x < 2. Find the solution for y

Solution :

x + y > 0 Þ 0 < x + y    ....(1)

Also, x < 2                    ....(2)

Adding (1) and (2) we get,

0 + x < x + y + 2

(Subtracting x from both the sides)

Þ 0 + x - x < x + y + 2 - x

Þ 0 < y + 2

(Subtracting 2 from both the sides)

Þ 0 - 2 < y + 2 - 2

Þ - 2 < y or y > - 2


Example 9

Solve

Solution :

Note that If a > 0

1) | x | = a is equal to x = a or x = - c

 

 

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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