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-‘Guppter= 1, RELAPtONS AND. FUNGTEONS
‘dahon ena - at A de Gs nam ni wt. un a_Julaten_
Sw 6} d_nolahon:- bt A,B by tp ify amo dot Rb
a_nolalion ast Ano stB
Shon thi woe} RK donot by R's solatien
ftom _6 Aon 1s _dijmic —by f
=] (bea) (ab) ERY :
(ab)ER <> (ba) ERT
Dom(R) = Range (R*) and, :kan(e)=. Oom(®)
Wes OF RELATIDNG *-
Veld —_slahon °- WA hg dit Shon d © AXA nd ap it
a mulation en A- This swlahen tw alld
te -uoid | imi wahon: on pk A.
) Ural wleton AXA SAXA re, jk gach dymmt GA ip
nila td tue Si ee
")Scombty —sulahon +S wy dument G Aas. milo
i lull only.
Ty Weal: ait,
= 3 f Ths Date “> &
i a
| —=—
ar ae wolion’ A wlahen Ron 0 wt Aw ond hp
fi | —— Jywa sp wut alyma ad saa
0 _ttou: {
Ris Reriexwe & (0,0) Ek pproallhaéeny
v) | dumm olahion:- A wlahon kono sKA wo ona i
|? bra diwmmbic julohen if,
(apleR > (ba) ER for al iained prey Vn
akb> bRa for all adDEA
v) Tuometuwt folations- A wwlahon k en Aw onid | bg
namollius wlaion. ip
[aby ek and (b,c) ER 3 oie jor all lobeeh se,
y
weaRb- andr bRE TRG) focal a haem
A) ANTISYMMETRIG RELATION &
> A lah Ron wt A ip said tp be am amnftournarutuc
nélahon iff °
” (able and (ba) eR 3 a=b forall bea
yore | S(abyek bu (ba) @R tun abi nami ‘antigym—
Lh rwlation. r
WIE SUIVALENGE RELATION %-
SA nuahen Rona st Ab sold m be an anu
machen on A yy iF iy Dent, ume
classmate.
Date ¥
Q_ounycion jf suum, demand oy Bd Hu fmnage | cam
domunf oj Are, f(A) =8 ov rong ot 4p
demain 6+ d
FA28 i owe if} for ech beB > TOE a
Two FUNGTIDN 3-
A junchon {2 A=8 1) am im funchon if thu iui an
lumen! yn "6 hung no Ime—amage am A
BIJEGTION [ONE -oNeE oT FUNCTION 3-
A_funchon 4+ AB ip a Dyction ut tp ome -or®
elo t ‘
COMPOSITION OF FUNGTIONS
hen qq] AWC apna by ‘foot
lt f:A>6B and 4: Bc fumchons ay a _funt-
9 (4
oalit—ngaton 4 | oh 9 :
Qo} “iat whin namgn_ er oubst of the dom-
| an @4,,and nang,” gf < demain A:
PROPERTIES OF GOMPOSITIDN OF ee:
T ? ii att
Shum 2) Thy cemfaailion Ot functions
1 agg Ie 9 |
hou “thu functions: och. “hol (fog)on_and ai
yuk, then (foa)oh « fo[goh).
Shupum-3
du_componition 4 Du lun buice gn. re
and_q aio nego an
Jupum-+), Lt ot hun id tie dt _compoorion ua
function wih ty” dumb fur bh fumelon
Shug 5) Ut Ff: AB 44 BoA hh a fumchony ouch tha} Qa «Ta |
dun, fb fan umychion andy a_pittychon
Shuma
lit PH A?B and 4+ 6—>A by fu funchorw owh that.
oq = Te Jun, f a ourycten and 4) am mycin. _|
Dupiwm -7/ Lt qiA= B and 4 b> ¢ —b TD pa shun
gt’? Ap~Cw ond > 4. > C i ont
W)
Go}: A>C_ mu-or 3"q¢A—>8 0 gni-ond
iy
qh: A>C yy ono amd g: 48°C BW omen a fA> 8B is om.
iv)
Sot A?C 1) pm- one ‘nd | R98 yp on 34:80
Jom -one.
~—__#)| Gomensi TN Of REAL FUNCTIONS %
Sur p> cond 4+ De? RK be tutu jc
={2e0, 4) E02) Rk a. ah Y= {1EDa 9 fae
The enya e au sufi ao goy lr) Ga) "fralveex
|
Lamd_foq(n) = }(g()) rey. a
SSP
Note)i) 41 Rama () = Dem ys of: Dik and 1 if fan(q) ¢
Dom (4)! thon fog. : ee
J
J] f:R>R and gq: ke gu mal funchionds . thu foq
and qo) both "ia.
INVERSE OF A FUNG TIDN $-
lt {:A>B dea byechan dwn o fumchon a: BA hich
Csvcuil toch “erred UeB Da uminud dumont eA
ouch that Mele altuna, “a
PROPERTIES OF INVERSE OF A FUNGTION % -
) Shi imu. 9 0 buyichom 1 umiqe.
2) Th imunnas a dbuchon aloo a byedion
