Page 11 - DECO403_MATHEMATICS_FOR_ECONOMISTS_PUNJABI

fJekJh^1 L cbB

d{i/ PpdK ftZu, B'N

i/eo X ns/ Y d' nfoes ;w[Zu j'D ns/ fe;h fB:w f d[nkok X dk
jo/e nt:t Y d/ e/tb fJZe ftbZyD (unique) nt:t Bkb i[V
(associated) j' ikt/ sK d'uo ;zpzX (binary operation) R, X dk Y ftZu

∈
y
x
fJ; soQK R = {( , ) : x ∈ X , y Y B{z X dk Y ftZu cbB efjzd/ jB.
}
T[dkjoD ti'A^i/eo X = {1, 2, 3}, Y = {3, 4, 5} sK fB:w y = x + 2 d[nkok X d/ nt:t 1, 2,
3 eqw nB[;ko Y d/ nt:t 3, 4, 5 Bkb r[fDs j'Dr/. fJ; bJh d'uo ;zpzX R = {(1, 3), (2, 4)
(3, 5)} B{z X dk Y ftZu cbB ejKr/ ns/ fJ;B{z
: fX → Y iK X →
f
Y
th fbyd/ jB. fJ; soQK cbB f fJZe fB:w j? fi;d/ nB[;ko X dk jo/e nt:t Y d/ fJZe
ftbZyD nt:t Bkb r[fDs j[zdk j?.

1H9 cbB dk v'w/B iK gqGkt y/so ns/ gok; iK o/Ai
(Domain and Range of Functions) .

i/eo cbB fX → Y s'A gfoGkfPs j? sK ;w[Zu X fJ: gqshfuZsoD iK cbB f dk v'w/B iK
:
gaqGkt y/so (Domain) ejkT[Adk j? ns/ ;w[Zu Y fJ;dk gok; iK o/Ai (Range) ;fj^gqGkt y/so
(Codomain) ejkT[Adk j?.

cbB f dk gqGkt y/so (Domain) = x d/ T[jBK ;ko/ n;b wkBK dk ;w[Zu fiBQK d/ bJh cbB
gfoGkfPs j?.
cbB f dk gok; (Range) = gqGkt y/so (Domain) dhnK ;kohnK okPhnK x d/ ;zrs, y d/
wkBK dk ;w[Zu.
T[dkjoD ti'^y = 2x + 1 ftZu y, x dk cbB j?. i/eo x fJZe s'A tZv/ ns/ gzi s'A S'N/ XzB g{oD
nze wkB rqfjD eo/ sK cbB dk v'w/B iK gqGkt y/so ;w[Zu {2, 3, 4} j'fJnk ns/ T[d'A cbB dk
gok; ;w[Zu {5, 7, 9} j'fJnk. fJ;h soQK d'uo ;zpzX R = {(5, 8), (6, 9), (7, 10)} dk gqGkt y/so
;w[Zu {5, 6, 7} ns/ gok; ;w[Zu {8, 9, 10} j'fJnk.

i/eo cbB f d/ gqGkt y/so dk fJZe sZs x, gok; d/ fe;h sZs y Bkb r[fDs j? sK gok; d/ fJ;
sZs y B{z, fijVk x Bkb r[fDs j?, f(x) Bkb gqrN eod/ jB, fiZE/ f(x), x d/ bJh cbB f d/ wkB B{z
do;kT[Adk j?.

: fx → B{z f : x → f(x)
y
d/ o{g ftZu fbfynk ik ;edk j?.

1H10 cbB d/ gqeko (Kinds of Functions)

1H fJZeuoh cbB (Functions of Single Variable)^i/eo uo okPh y e/tb fJZe uo okPh
x s/ nkfPqs j?, T[d'A y = f (x) fJZeuoh cbB ejkT[Adk j?. fJ;h soQK, y = f (θ), s = f (t),
v = f (t) nkfd fJZeuoh cbB jB.

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