Page 20 - DECO403_MATHEMATICS_FOR_ECONOMISTS_PUNJABI

noEPk;soh dk rfDs

2
B'N jZb L feT[Ai' 2 nzsokb (^2, 3) ftZu j? fJ; bJh fJZE/ f (x) = x – 2
2
∴ f (2) = (2) – 2 = 2
feT[Ai' 4 nzsokb (1, ∞) ftZu j? fJ; bJh fJZE/ f (x) = 3x – 1.
∴ f (4) = 3.4 – 1 = 11.
2
feT[Ai' ^1 nzsokb (^2, 3) ftZu j? fJ; soQK fJ;d/ bJh f (x) = x – 2.
2
∴ f (–1) = (–1) – 2 = 1 – 2 = – 1.
feT[Ai' ^3 nzsokb (^∞, ^2) ftZu j? fJ; soQK fJ;d/ bJh f (x) = 2x + 3.
f (–3) = 2 (–3) + 3 = –3. T[Zso

T[dkjoD 21H cbB (- 2) (4-)x x dk gqGkt y/so gsk eo'.
jZbL wzfBnk

−
( ) = (fx x − 2)(4 x
)
id'A x > 4, sK ( ) = fx foDkswe okPh
& ekbgfBe okPh

id'A x < 2, sK ( ) = fx foDkswe okPh = ekbgfBe okPh
fJ; soQK 2 ≤ x ≤ 4 d/ bJh jh f (x) n;b j?.
∴ (x − 2)(4 x dk gqGkt y/so & 2 ≤ x ≤ 4H
−
)
T[Zso
T[dkjoD 22H i/eo f : x → x +3 ns/ gqGkt y/so = {x : – 2 ≤ x ≤ 2, x g{oD nze j?} sK
cbB f ns/ T[;dk gok; gsk eo'.

jZbL
f dk gqGkt y/so & {x : – 2 ≤ x ≤ 2, x g{oDnze}
& {–2, –1, 0, 1, 2}

f d/ gqGkt y/so dk jo/e nt:t f cbB d[nkok x + 3 Bkb r[fDs j[zdk j? fJ; soQK
nt:t ^2 cbB f d[nkok ^2 O 3 & 1 Bkb r[fDs j?.
nt:t ^1 cbB f d[nkok ^1 O 3 & 2 Bkb r[fDs j?.
nt:t 0 cbB f d[nkok 0 O 3 & 3 Bkb r[fDs j?.
nt:t 1 cbB f d[nkok 1 O 3 & 4 Bkb r[fDs j?.
nt:t 2 cbB f d[nkok 2 O 3 & 5 Bkb r[fDs j?.
fJ; soQK cbB dk gok; & {1, 2, 3, 4, 5}
ns/ cbB f & {(–2, 1), (–1, 2), (0, 3), (1, 4), (2, 5)}H

gqPBktbh

1
2
1H i/eo f (x) = x – 1 sK f;ZX eo' fe f (x) + f  = 0H

x
x 2 
1
n 
fn
2H i/eo ( ) = sK ( ) + fn f  dk wkB gsk eo'. [T[ZsoL 1]
1 n+ 
n
3H i/eo f (x) = log e x sK f (1) dk wkB gsk eo'. [T[ZsoL 0]

14 LOVELY PROFESSIONAL UNIVERSITY