Page 14 - DECO403_MATHEMATICS_FOR_ECONOMISTS_PUNJABI

noEPk;soh dk rfDs

B'N

fiZE/ S ;wheoD g(x) = 0 dk jZb (solution) ;w[Zu j?. d{i/ PpdK ftZu S nfijk ;w[Zu j? fe

Gkt
;gPN j? fe f/g dk v'w/B D∼ S j? Gkt D ftZu'A T[jBK nt:tK x B{z eZY fdZsk j? fi;d/ bJh
g (x) & 0H
1
, B{z d' cbB jB T[d'A ()fx ns/ ()xφ
T[dkjoD ti'A^wzB fbU ()fx = ns/ ()xφ = xx d/
2
x
1
phie :'r B{z ()fx +φ () iK ( f+φ )( ) Bkb ;{fus eoKr/ ns/ ( f+φ )( ) = + x j't/rk.
2
x
x
x
x
1
d[pkok cbBK d/ r[DK B{z ( ).fx φ () Bkb ;{fus eoKr/ ns/ ( ). ()xφ = x ⋅ 2 = x j't/rk.
fx
x
x
φ
φ
x
x
f { ( )}, x d/ fJZe cbB d/ cbB B{z ;{fus eodk j? fiZE/ f,φ () dk cbB ns/ fco ( ),xx
dk cbB j?.
jZb ;fjs T[dkjoD

T[dkjoD 1H eh fBwBfbys cbB jB<

jZb L (i) i/eo x dk e/tb fJZe wkB XzB iK foD fbnk ikt/ sK y = x cbB j't/rk. i/eo
d'B'A wkB fJeZm/ bJ/ ikD sK cbB BjhA j't/rk.
3
(ii) x d/ jo/e wkB d/ bJh x + 5x dk fJZe fBPfus ns/ ftbZyD wkB gqkgs j[zdk j?.
fJ; soQK fJj fJZe cbB j?.
(iii) R cbB BjhA j? feT[Afe ;w[Zu X d/ nt:t 2 dk r[DB ;w[Zu Y d/ nt:t 3 ns/ 11
s'A j' fojk j? id'Afe X d/ jo/e nt:t dk r[DB Y d/ fJZe fBPfus ns/ ftbZyD nt:t s'A j'Dk
ukjhdk j?.
1
T[dkjoD 2H x − 1, Bkb gfoGkfPs cbBK dk v'w//B gsk eo', fiZE/ x n;b
2
3
x − 1
;zfynk j?.
2
jZbL (i) f (x) = x – 1 ftZu x d/ jo/e n;b wkB d/ bJh f (x) dk fJZe fBPfus n;b wkB j?,
fJ; soQK fJ;dk v'w/B ;w[Zu R jh j?.
1
(ii) ()fx = ftZu x = 1 d/ bJh f (x) dk wkB nfBPfus j? gozs{ i/eo x d/ wkB
x − 1
3
pkeh n;b ;zfynktK j'D sK f (x) dk th wkB n;b j?. fJ; soQK fJ;dk v'w/B R ∼ {1} j?.
x 2 − 4
T[dkjoD 3H i/eo x n;b ;zfynk j? sK cbB f(x) = dk gqKs (v'w/B) fBPfus
x − 2
eo'.
0
jZbL id'A x = 2 sK f (x) dk wkB d/ o{g ftZu gqkgs j[zdk j? fijVk fJZe nfBPfus wkB j?.
0
fJ; d/ fJbktk x d/ jo/e n;b wkB d/ bJh f (x) dk fJZe fBPfus n;b wkB gqkgs j[zdk j?.
fJ; bJh cbB dk v'w/B 2 d/ fJbktk ;ko/ n;b ;zfynktK dk ;w[Zu j?. ;ze/s o{g ftZu
D(f) = R∼ {2}.

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