modulus vnr
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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
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