Page 9 - DECO403_MATHEMATICS_FOR_ECONOMISTS_PUNJABI

fJekJh^1 L cbB

uo okPhnK d' soQK dhnK j[zdhnK jB^ B'N

(i) ;[szso uo (Independent Variables)
(ii) nkfPqs uo (Dependent Variables)
i/eo d' uo okPhnK x ns/ y go;go fJ; soQK ;zpzXs j'D fe fJZe uo okPh x B{z ;t?^fJZSk s'A
e'Jh th wkB d/D s/ s{ih uo okPh y dk wkB T[; T[Zs/ nkfPqs j't/ sK x B{z ;[szso uo
(Independent Variable) ns/ y B{z nkfPqs uo (Dependent Variable) efjzd/ jB.
T[dkjoD ti'A^wzB fbU y 2 = x 5 + H

j[D uo x B{z ;t?^fJZSk s'A fGzB^fGzB wkB eqw nB[;ko 0, 1, 2, HHH d/D s/ ;kB{z y d/ fGzB^fGzB wkB
eqw nB[;ko 5, 7, 9, HHH gqkgs j[zd/ jB, fijV/ ;gPN o{g s'A x T[Zs/ nkfPqs jB.

fJ; soQK fJZE/ x ;[szso uo ns/ y nkfPqs uo j?.

1H3 cbB (Functions)

cbB dk f;XKs d' go;go ;zpzXs uo okPhnK (Related Quantities) T[Zs/ nXkfos j?.
wzB fbU fsoi:k r d/ fe;h r'b/ dk y/socb A j?, T[d'A
2
r
A =π
fJZE/ okPh r ;[szso uo (Independent Variable) ns/ okPh A nkfPqs uo (Dependent
Variable) j?, feT[Afe r'b/ dk y/socb A T[;dh fsoi:k r T[Zs/ nkfPqs j?.

fJ; dPk ftZu n;hA efjzd/ jK fe uo A, d{i/ uo r dk fJZe cbB j? fi;B{z rfDs dh GkPk ftZu
fJ; soQK fby e/ ftnes eod/ jB^

A = ( f r)
Gkt [A cbB j?, uo r dk]

1H4 cbB dh gfoGkPk (Definition of Functions)

fJZE/ d' uo okPhnK x (;[szso uo) ns/ y (nkfPqs uo) fe;h fB:w ‘f’ d/ d[nkok fJ; soQK
;zpzXs (related) j'D fe x d/ jo wkB d/ bJh y dk fJZe fBPfus ns/ ftbZyD (unique) wkB
gqkgs j't/ sK y B{z x dk f ^ cbB efjzd/ jB fi;B{z y = f(x) fby e/ gqdofPs eod/ jB.

x d/ cbBK B{z f(x), g(x), φ(x), HHHH nkfd gqsheK d[nkok gqdofPs ehsk iKdk j?.

1H5 cbB dh ftnkfynk (Explanation of Functions)

i/eo y, uo x dk fJZe cbB j? Gkt y = f(x)H
T[d'A x B{z ;[szso uo (Independent Variable) ns/ y B{z nkfPqs uo (Dependent Variable)
efjzd/ jB.

i/eo y = 5x + 7 sK x d/ jo wkB d/ bJh y dk fJZe fBPfus wkB io{o j?. i/eo y B{z x dk cbB
efjzd/ jB.

1H6 cbfBe ;ze/sB (Functional Notations)

fJ; sZE B{z gqrN eoB d/ bJh fJZe uo^okPh y, fe;h j'o uo^okPh x dk cbB j?, pj[s ;ko/
;ze/s gq:'r ftZu fbnkJ/ iKd/ jB. ;G s'A tZX gq:'r ftZu nkT[D tkbk ;ze/s j?L
y = f(x)

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