Page 21 - DECO403_MATHEMATICS_FOR_ECONOMISTS_PUNJABI

fJekJh^1 L cbB

x B'N
4H cbB f (x) & dk v'w/B (domain) ns/ gfo;o (range) gsk eo'. eh cbB Jekeh
+
1 x 2
j?< [T[ZsoL R]

a
f 
b
x 
fx
5H i/eo ( )= sK dk wkB gsk eo'. [T[ZsoL (-a/b))]
x − 1 
b
f 
a

x+ 2
( ) H [T[ZsoL (-a/b))]
( ) =
6H i/eo y = f x sK f;ZX eo'A fe x = fy
x − 1
2 3x −
7H i/eo ( ) = sK f;ZX eo' fe f (x). f (–x) = 1H
fx
2 3x +
x
8H i/eo f (x) = e sK f;ZX eo' fe f (x + y + z) = f (x) . f (y). f (z).
1   1 2 
1
2
9H i/eo ( ) = fx x + sK f (–1) ns/ f  dk wkB gsk eo'. [T[ZsoL 2,  + x 
x 2   x 2 
x
9
4
3
2
7
6
8
10H i/eo f (x) = x – 6x – 2x + 12x + x – 7x + 6x + x – 3 sK f (6) dk wkB gsk eo'.
[T[ZsoL 30]
11H x d/ feBQK wkBK d/ bJh fBwB cbB gfoGkfPs BjhA jB<

2
12H i/eo f (x) = 3x + 2 ns/ g(x) = 2x + 5, sK fBwBfbys d/ wkB gsk eo'^

13H i/eo A = {a, b, c, –1} sK dZ;' fe eh fBwBfbys ;zpzXs ‘A dk A ftZu’ cbB j?. ekoB th
dZ;'L

14H

sK f (3), f (12), f (–15) ns/ f {f (5)} dk wkB gsk eo'.

15H i/eo g : R → R fiZE/ g (x) & [T[ZsoL 20, ^2, ^4]

ftZu g (5), g (0) ns/ g (-2) dk wkB gsk eo'.

3, id'A –3 ≤ x < –1

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