Page 10 - DECO403_MATHEMATICS_FOR_ECONOMISTS_PUNJABI

noEPk;soh dk rfDs

B'N fi;B{z fJ; soQK gfVQnk iKdk j? fe “y pokpo j? x d/ cbB d/”.
j'o ;e/s jBL y = F(x), y =φ(x), y = ψ(x), HHH, nkfd.

eh s[;hA ikDd/ j' i/eo fJZe uo okPh x d/ fe;h wkB d/ bJh d{ih uo okPh y dk fJZe s'A
tZX wkB j't/ sK y, x dk cbB BjhA ejkT[Adk pbfe y B{z x dk ;zpzX
2
(Relation) fejk iKdk j?. T[dkjoD ti'A y = xH fJZE/ x d/ jo wkB d/
bJh y d/ d' wkB gqkgs j[zd/ jB. nfij/ ;zpzXK B{z edh^edh tZyA^tZy
wkB cbB (Multi-valued function) th efjzd/ jB.

1H7 cbB dk wkB (Value of Functions)

wzfBnk uo x dk e'Jh cbB y = f(x) j?.
f(x) ftZu x = a oZyD s/ f(a) gqkgs j[zdk j? fi;B{z x = a d/ bJh cbB dk wkB efjzd/ jB.

X = a T[Zs/ f(x) dk wkB = f(a)

fijVk f(x) ftZu x d/ ;EkB s/ a oZyD s/ gqkgs j[zdk j?.

2
T[dkjoD ti'A^wzB fbU f(x) = 2x – 3x + 5
2
T[d'A f(2) = 2(2) – 3(2) + 5, [x d/ ;EkB s/ 2 oZyD s/]
= 8 – 6 + 5 = 7.

;t?^w[bKeD (Self Assessment)
1H ykbh ;EkBK dh g{osh eo' (Fill in the blanks)-

(i) gfotosBPhb okPhnK B{z HHHHHHHHHHHH efjzd/ jB.
(ii) T[j okPhnK fiBQK dk wkB rfDs dh jo fefonk ftZu ngfotofss ofjzdk, HHHHHHHHHHHHHH
ejkT[Adh j?.
(iii) nfijhnK d' okPhnK fiBQK ftZu fJZe d/ pdbD s/ d{ih th pdb iKdh j?, T[j HHHHHHHHHHHH
okPhnK ejkT[AdhnK jB.

(iv) r'b/ dk y/socb T[;dh HHHHHHHHHHH T[Zs/ fBoGo eodk j?.
(v) fiBQK okPhnK dk wkB jo gqPB ftZu ;fEo j?, HHHHHHHHHHHHHHHHHH ejkT[Adh j?.

1H8 wkBfuZsoD d[nkok cbB dh gfoGkPk
(Definition of Functions by Mapping)

i/eo nfoes ;w[Zu (Non-empty set) X d/ jo nt:t x dk r[DB (Correspondence) nfoes
;w[Zu Y d/ fJZe fBPfus ns/ ftbZyD (unique) nt:t y Bkb fe;h fB:w f d[nkok j[zdk j? sK
f B{z ;w[Zu, X B{z ;w[Zu Y ftZu wkBfuZsoD (Mapping) fejk iKdk j? ns/ fJ;B{z Bkb
gqdofPs eod/ jB. fJ;h wkBfuZsoD f B{z cbB efjzd/ jB. wkBfuZsoD d' ;w[ZuK X ns/ Y B{z
nt:tK d/ ftZu r[DB d/ finkfwsh gfjb{ B{z gqdofPs eodk j? ns/ cbB fJ;dk ftPb/PDkswe
gfjb{ gqdofPs eodk j?.

4 LOVELY PROFESSIONAL UNIVERSITY