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(2) ( g o g ) : R ® R is given as :

     ( g o g ) ( x ) = g [ g (x) ]

     = g [ x2 + 1 ] = (x2+1)2 + 1 = x4 + 2x2 + 2

(3) ( g o f ) : R ® R is given as :

     ( g o f ) ( x ) = g [ f (x) ] = g [ x3] = (x3) 2 + 1 = x6 + 1

(4) ( f o g ) : R ® R is given as :

     ( f o g ) ( x ) = f [ g (x) ] = f [ x2 + 1 ] = (x2+1)3

Example 3

If f(x) = log x and f (x) = x3 , show that
f [ f (2) ] = 3 f (2)


Solution :

L. H. S.

f [ f (x) ] = f [ x3 ] = log ( x3 ) = 3 log x

Put x = 2 then f [ f (2) ] = 3 log 2

R. H. S.

f ( x ) = log x Þ f ( 2 ) = log 2

\ 3 f (2) = 3 log 2

\ L.H.S. = R.H.S.

Example 4

If f (x) = x7 - 5x5 + 3 sin x show that
f (x) + f (-x) = 0

Solution :

f (x) = x7 - 5x5 + 3 sin x is an odd function

\ f (-x) = -f (x) = - [ x7 - 5x5 + 3 sin x ]

\ f (x) + f (-x) = 0

Example 5

If f (x) = ( Öx )x show that

Solution :

f (x) = ( Öx ) x Þ

 

 

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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