THE MODULUS FUNCTION

AN INTRODUCTIONV.NAGARAJAN

PGT-MATH

Definition

0

0

The modulus of , denoted by , is defined by

, if ,

, if .

x x

x x x

x x x

( ) ( )

( ) ( ) ( ) 0

( ) ( ) ( ) 0

The modulus of , denoted by , is defined by

, if ,

, if .

f x f x

f x f x f x

f x f x f x

)3)(2)(1()( xxxxf

)3)(2)(1()( xxxxg

)sin()( xxh

1)( xxf

11)( xxg

321)( xxh

Some properties

,baba

numbers, real are and If ba

),0 that (provided , bba

ba

.baba

Some equivalent statements

0If , then is equivalent to .a x a a x a

0If , then is equivalent to .a x k a k a x k a

Do Q1-Q4, p.23

Squares, square roots and moduli

,2 xx

,222 xxx

, and realFor ax

,22 axax

,22 axax

. ,0 if 22 axaxa

Squares, square roots and moduli

,2 xx

,222 xxx

, and realFor ax

,22 axax

,22 axax

. ,0 if 22 axaxa

DO EXRCISE IN NCERT TEXT BOOK