Support the Monkey! Tell All your Friends and Teachers

Help / FAQ


Example 7

If f(x) = x2- 2x + 3, x Î R. Find the values of x for which f(x) = f (3x - 1)

Solution :

f(x)    = x2 - 2x + 3 Þ f (3x - 1) = (3x - 1)2 - 2 (3x - 1) + 3

= 9x2 - 6x + 1 - 6x + 2 + 3

= 9x2 - 12 x + 6

\ f(x) = f(3x - 1) gives us

x2 - 2x + 3 = 9x2 - 12x + 6

8x2 - 10x + 3 = 0

(4x - 3) (2x - 1) = 0    ...(factorizing)

4x - 3 = 0 or 2x - 1 = 0

\ x = 3/4 or x = 1/2

\ The required values of x are 3/4 and 1/2


Example 8 An open box is to be made from a rectangular piece of tin 12 cm ´ 12 cm, by cutting four squares from each corner and turning up the sides

(1) Find the formula that expresses its volume

(2) Find the domain of the function expressing its volume

Solution :

(1) Let x cm be the length of the each side of this square to be cut off and V be the volume of the box. Then the dimensions of the open box are as - Length = (12 - 2x), Breadth = (12 - 2x) and height = x in cm.

\ volume of the box (V) = Length ´ Breadth ´ Height

\ V = (12 - 2x) . (12 - 2x) . x cm3

\ V = (4x3 - 48x2 + 144x) cm3

(2) put v = 0 Þ (12 - 2x) (12 - 2x) = 0 Þ x ,= 0 or x = 6
    (cut points)

Interval

Test values

Values of f(x) i.e. V

Sign of f(x) i.e. V

(- ¥ , 0)

-1

(10) (10) (-1) = - 100

-

(0, 6)

5

(2) (2) (5) = 20

+

(6, ¥)

7

(- 2) (-2) (7) = 28

+

Since the interval (6, 8) is practically impossible (say absurd), the only acceptable interval is (0, 6) i.e. the domain of V is 0 < x < 6

 

 


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





All Contents Copyright © All rights reserved.
Further Distribution Is Strictly Prohibited.

905 PinkMonkey users are on the site and studying right now.