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درس الدوال - 2 ثانوي

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0% found this document useful (0 votes)
48 views9 pages

درس الدوال - 2 ثانوي

Uploaded by

saliilian2028
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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g
Re 503
8() C f(y E :

Df
f(04) 8(2)
=

:
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C
88-7 :
fl =
20
f(0) =

f(m) :0 of
>
-
me
=
[q + * (
-

f(2) Et
m
=

f(w) =
ma + 6m + 2 ·
S ·
J

f(1) 1a 6() 2
= + + -
f() =
9
f(r) =+ 3

f( 2) (2) 6 (2) 2
- = + + -
-

f( 2) = -
6

f(s)) (*

si
Si
6(2)) 2 f(x) 5 Gu

to
= + + - = +
-
wF - 2 =8
T
=
gw+

·
2

22
f(u) = 2 - mi + 6n +

wa + Gw +1 -
= 0 3 0 .
-3 [5] .
31 . 2703-2 , + 8[

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0. 3[U] 3 220] - Lit


-

.
fis

w(w 6) + = 0 ·
2j
-69026j2 ji f(u) 2 m
LpWE SN O
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wa + Gm + 2 = 7
- w -

4 30 ·

di Fdjj
w+ 6 m 2 +7 5
+ = 0
wXH :

(D) dom += 0 En + 016851& dis)ji &


+f
- -

-
8

# + xm += 0

Co ( + 3)a = 0 Ay ·dld .-H


N + 3 = 0 2
42
15

Mot-3 o
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3 add -

71

f(m) =
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3

S am
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2wa +
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jsli ! =
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S
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20
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3 3Y
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8h
A

f=9 de
J

-m

-3 jigs
-

f(x) = - 0 - (w + 3) -
=
=

( 3)a + = - 8 +7

=
(49) =
4 as

& cons 6 Dflu) E = -o

·
5
E 51
3 -9 : 11 ,
a

Commentaines -
2 - 4 f(u) = m2
DJ = R :
49
% 151

f(w) = -

(m + 2)2 + 5
(+ b)2 a + ba = + 2ab-1 03
f(u) [ma + 24 2 2) 5

18o e
= -
+ . w .

f(u) = -

(02 4 4m) 5) + + + on
f( =
-whym
noum +1 . 4610s
· 2

Estigt(b) fla/f(b) :
o a <b

·. 2 -
2 f() =
=5
-2 ·
b 2 -
21 + D/
307
3- 0 07
.
J851902 :fo
2 & To 30 . + 82 -f
(2)
+ - -

> 0 a+ 27b + 2

D
-T
·
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( + 2)27( a)s +

+
(a + 2) y (+ 2)a

7
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=

·
Glitaljbl zjfl f 16
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-
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:
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Catal Jos100 : Festin


f
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o

Ay
(07)

1
Commentaie
=
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f(w) =h Tu · A

fla) = 13
flul-In) OfR ::disdd

In
S
-
1 + 3(0 2)
f(u)
-

w -
2

1 + 3 6
f(u)
I
In
-

w - 2
"

idb 42/

# fl
&
:
...
61 lis
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mu
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.
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a
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Si ~

#
ji 30 .
+ 0 685/
273752 +3

T) -
e9 ·
%1 51 g
s

g(u) =
n + 3 f(y = m -
2
=R j5gjgsf · 89 .. --
S

: fxgiftg :
dip soig fin Jo
·
,

f(w) + y = ma -
2 + 4
Df Dg Distingo i =

=
na + 2
Auen f( g(y) : D gw8% je
= .

S
.

m
f Si,
f(u) g(u)
2 3
g
+ = -
+ m + =

=
m2 +
m + 1 n + 3
+ 00w +3 :
=
f(u) xg(u) (m -+3) Ru 2 33 g(y) (w 3) f() = -Gm 9 :
gsfj/b
CE
= = -
- = - +

-
3w
= n + -
2w .
6v =
3 -
0 .. 3[8] -
3, + 0[ : jus gsf
:
Asbl
j .
3
Ag RusDf
= = R :S :
Df Ag = :
goria
/Dg s Df jjgjh gof ·s Co- Df Dy
= :
&s

gof Blog 5 f % 11 . g(u) =


(w -

3)2( b) - = a + b2ab :
5 flu gla) Q = :

(0f)(n) g[f(u] Dyof SwedfifheDg3 :0 :Is


= := = = m + 33 .

ma + 9
=

-
6m

: D
-Gr + 9

g(u) = m
f(u) = m -
3
pg ,
Djgsfiddl .d fl g() : =
s
me nj
&
·

meDf :
f() EDg f g :/blj
=

Dgowogof (r) =
gYu]] g(u) = m

g(t) = : 2 j

·
= · f
g(a) g ,

j
WER g(z) = 5 Cj s n j +(6)
MEDf -o

370
3Dg w -

-e
m -

3

=
D

fog () f(g(z) =

Dgof B = . + -[ -
3

g(f) -
3
f(4) =
1
Dg = R
Af R [1 ja !
s - -
:

= -
f(5) =
2

wa
·j sibljisDfDy
m
:
jus

flu) - Df R 31]
-

= = -

f4) = DJ m-1)

gl-iDg
= R = -

-m
gof(y =

g4f(n)
:/ - 1 .
2

WEDL - WE R siDg , fjgj5gsf


m -

330 >
-

wx3iDgof =
( , + 0(
sin ?
:1951d

: 2 di Df ( + 1) (2) =

f(2) kf + + 14 , 8295
g fl : R & jgof DfnDg( g)(y + =
f(z) g(y) f + +
g 908253
gof (2) =

g(f(x)] fog() f [g(2)] =

Df (4f)(m) f(t) = 1 .
4
f edifsls
.

3f(u) 2
Df1 Dy (xg(() f(y xg(t) fig fil)
e
+
g
= =
,

=
3(m 3) -
+ 2
meDfDg gly +O
:
(H = f
5 gaf
=

=
3n

3w
- 9+ 2

-
7
= 3 -
1

S
gog() g(g(a)
fof(y) f(f()
=

=
3g(a) + 2

&
=
3
(3n + 2) + 2
6 2
= 9n + +

&
4 = 9n + 0
: 6

g() = m+ 3 =
f() = m -
3 = Rj9jg f s
:
J1 5jo] ,

fge f ginobi &o +


fly =
V
>
-

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3/ mx] + 5

in
8
= 2m M 0 N + 2 · + 22

fl g() = Ec ! Do On &8 1
UN
+ w :

f=
.

R 05tig
feg&blj 0 a) 0 ji
:

·
:

flu) xg(x) =
(m 3) -
x (n 3) (a b)(x + b)
+ - = a b2 -

f(x) =

( -
3)8 + 1

na 32 W
r
=
-

= n2-9
in on2 + 1
*

8h xgla) : : Don 4 % (4) n


= + 3

if g +
i

j 0 J4gl =
gal :
fegNIsidiss + (a) =
ma +
13 flu =
Vouin)

& 5 ds) a) /S 0

Mo
3-0,0] Jeuvjfxg s
84) =
catol poste oui
cig
0x
·
n

: G Jo rSy fl) =
Vouz)

fly =A w 8 7 -
0,1) & :gnid-f

20 fid .d
8 1 51
.
:

, + ,

3 -

0. 2) 68518 fids oigno ·


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flu = T f+ k =
f
+
-
f + 4

w() 24 fo -
f+ k

t
w -
2w + 4 >
-
u

O UL)-H-son ) 1
8 : 10 - 8 -Xf0
E r(x
.

fl) 800Nfo
wq
Vow(n) =
=

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20 + 0C Z weDui UEDr

·
No - 80 - 4fo
WEDr w(2 --2wY -4 o H-2w) -
y +
fo &fo
H-2mX ,
0
me

:ffogzin
THEDO :s /0 fog l in

y = Vou : ·n fog
fago lobil d
· 8 +
&b =

i- f
2 j 33UH fl go foga
= 4 - 8m + =

3 -
0. 2) J :51

Estigjolis 0 =
el
f +
g
=
f ",g -
fogt
70 +[ 6851880 ;
fr ;
g ->
f g)+

Il
-j
fig 3
.

Essisen
·
62 =1da

·
fl) =
2m
f mo
+

(a
fl = x ·

↑ d (f)jj ((g) j . g(u) f(n b)


= + + 4 = - -(2)

= + (1/4

( -) 4.51420.

& jj 11ij ( (2)


&/ ! Fin

·
·

fu=m
e w2

·- +
=

g(w)

(w ,
y) =
(0 ,
2 ,
5) DY sy

&
(X X) . ; ( , [15) 1J

&

-fr w

w = X + No
- On

X
y = +
y

-o
45
81
(44)
fu) =
( 2)
-
+

-
3 ..

ijjgg f() g(n 2)0


:
o = +
3

D
-

% (1) jjgge(x B) , c &" idf g(y) =


ma

f(29 -m) f(w) 0B + =


- -

[4 5do]((g) j (4)
.

f(x w) f(x w) 25
-
+ + = A
(3) +si
-2 +
/1 :blj s & 37
& ege g
-

· Jig :
: 3de
sy
f(n) =

N RS-1d J ·
flo
o

(1) sig711) tidie f() =

g(w -

y -
2
2 &B = 1

fa-w) f(w)
on
+ = B -
= ·i D
logl) =
F
27/
meD] -2-mEDfs MeDL Y' ( jld/51](918 (
-
:
,9

flofw N +

N
2

+ 1

(285005) -

1
+ =

25
- m n + 2
=
+
-
N - 1 n + 1

2
17
w m +
= + · : Is
N + 1 n + 1

w + w + 2
·
X
-edj (29) &x :
gla-Nifly : "Si !

= · J
· gdk
mi + 1

Dy

2 + 2
-
...
=

N + 1

i)
Ge
Ou

-
·
=
·j &
(1)jj)15 137
fh)
f(-2N
+ etli872tfl2 id :
Nigb( 1) =

25 (711 j 533 . *
B = 1
·
j, 50 8 Ah
un ) = 23
D

·
j - 1+
mag -
1
-me4i
n + ym + 3 . Do & f -

f +
fW) - =

(2/s 50
-
n =
2de
j ai
2
f w) =

f(m) -D =
(w + 1) (1)
tw)( y -
+
N
X=

H-mEAC Webf4 %
-

fl m)2
w + 1

2
1
m) 47 4 m) n
-

y - = -
4 -
+ -

+ 3 =

+
M Mu

=
ya +
m + 8w -
16 - 4m + 3

= 10 m + 3 I
wX + m
/
+

=
150 m ..
2
de g 20 f74- =

fl) jiss =
47/si & 1 1) -

, tiblois f(1-y (71 + + 2) = 2 : jiss

(1) S
-(w f(x =
+ m) ·
b

f() = no + 4m + 3 2+
meAfg 2-nEDf % d -

-L 1 ) -

, 1851js &it :

I
f(-2 m) (2m)
- = + 4) -
2 -
m) + 3 f(2 + m) =
( 2 m) + + 4 m)2+ + 3
+ g
=+ m -

~
=
1 + m +* 13 mm #B

= n2 -
S = n -
1

(9f5 ,
500 n-2 Je/s↓j:0
f(2 -m) f( = 2+
y 08%
:
fl) =
we
/ dj Y 1 + + 2

S
-

Xy+ -

jd Bi dis
V X 1
X 1&
+
m =
+ wo w = 1

-> E
=

Sy
-

X
X
+o
= +
y
X =

X7
) = m + 4m + 3

X =
X+ 1/X
X
X =
( 2) 4(X 2)
- + -

+ 3

X X2 m -+
=
X 0 -

= esig

X
X = -
1

X (X2
=

1 =flu 58
-

59871 1)
%(l)X-
, 151855gk
/48 slj s
X = X-
475j = ·

c es V X1bljas
Fidjij =

(4) 9 -j509w =
2
:c
post 15/
722w : P 5 blos
Pr =
2 -

+ 7
egesti de ·

deg G(y) deg P() = -

1
&
· Plu) & f(m) = anm" + An ... m +... + W .
n + Go

by i 2m 3m 5m
2 7 -
-
2 + 7 = 0 ·
Plus 1jax = 1
f(y) =
+ + + 1
degf = 5

3.
612
mo
P(w) =
(w a) G(w) - .
:S
f() = -
Sw + 3
degf =
2

&
( -1) (amo c) + bw +
& () =
3m2 + 5m + m -
1
deg f =
4

P b) //s ·
en % ,d
8 = m3 20 - 5n

·
7 27
② Sw am bm d
-
-

-
= + +
CN + + + 4
8

amen C = 1

o
1b
Ce
X 7x1 + 2 - 2x1 -
57x1 - 7
=
A l
=
ammam

94

-m +m + (c -

b) w
C= 2 1854 ·

b - a 7-b
= = - 5)
- C =
7 - c = - 7 (5)/1514 ·

P(m) =
(w 1) (2w2
-
- 5w -

7) P(m) (w = -

1) (2m2 5w
-
z)P(a)
-

=
(w -)(2n - 5w - 7) ·
et -so
·

·jb) =D /0 ~
c
- en
Si de · = 2m2 -
3 (m + m + w + 1 -
2 -

2w) -
3r -
5 -
10w + 1

am2 + bw c bic ER -
a
+ = 0 ,

a + 0
& 6 m -
7n-2
DegP = 3

cela -
:
39 Plusj
am + bw + c =

a[ =8. + ex)) juso

0 f(a) 0j81/feg /j
=
a adlj955

(w +bbr rigins J'a


· 81

f(w =

On a+ b +c + d = 0 + x = 1

(N +
bb = ·fabs je d = 1 j

f(1) = 1 -

2(1)8 - 5() + 6
Plu = &10
S -

an bw + + c =

a[( b + +
= 1 -
2 -
5 + 6

P()
2

=
-

0
1 -
1 = 0

6 = 1
= 0

-A
&c) j = 1 jis f = 0 dias

- b2 + Hac : 2 Je
Har
im P(1) = 4m 4m2 - 15 n + 18 =
( + 2) G(4) degg & am +bi +
Sebauas 3
-
·
=

Ya2
-18 8394/ Ph) (ja B . E P

D = ba 4ac am+ bw + c = 0 : :d , 14 · PL 2) -
=
4( - 2)3 -

4) -
a) -
1i) 2) -

+ 18
am2 + bm 3) jj
S

c +
4(-8)
+
= -

4(4) + 30 + 18
&in = c /d 289 !
=
- 32 -
16 + 30 + 18
b+ )
a(w m)(n wa) -b -30
-

-
-
W = ; wa = 0
& a

m D me Wa +8
cali P7)
-

PL) 5 jo -2 jias
a
.

= 0
·e
·

et
·

a(w -

m Wo = Wr = Nw
= D =
0 GliPh jas. jSi !
m -

D No to

P(w) (w 2) G(w)
Ya üjil
=

P a jk
- .

degg degp-S =

anttbm+c 0% R864551/0
W - - +

j ajj21s
J =
m + 55n -
4 : 1
J
-
m + 10m -
2570 . 2 fl 18: il..
S

100 4(1)( 2r) w + 10 m-25 d /b; wedi2


D = -
= 1 = 0 - -
= 0 :
f(m) -

4 :

No
= wo am10 er =-

.r & 7 jiz .
3

No =
5
64) =

a[(w +- bac] aib = -

-mouer
mu -
D
=

1[(w +525-4725
+ 1
= Y

5
: 03 &
-n + 10w -
20j0 ! S = 553
#
2m8-3m + 5 50 . 3 ·
2

4(f(5) 31/0002m3N
(w /20

I
D = 9 - -0 0 = - + 5 = 0 : / &>
G(w)3 4) -
+ :
jiss

RDedid
m -

8 T

23u + ↑ #
(N + -
5 = 0 :5/5
-
· tsd de
gisa (m +
50 flu) 3 -

47
m
ant + bw
· 31 95
-

+ c = 0 *

Nr
= i
wa =
-

·
f(u))m f :5 3

S wa-
.

-
S ms
-b
-
b
E
m2 Netwe =
=

+ = =

P wiXWz
=

=
&
a =
- b - -
b + saisie
La 5
W
z
=

-
=

f =


=
=

ba
a=2
;
b 3
=
; c = -
1 :
J
-

Ps 2m + 3n-1 = 0 :
de
c .
B g
d+ B = 80 -1

B
= il20 il a
·

: don
2 . B =
a - ·/ RI
mat2w-30 -
1

+ E =

2 D = b2 yac - D =
2 4(y)(3)

16
-
·+ 2m 3 = 0
Par m

b=2
-

c=
:

2
de / Ga

A =
a= -

-
ww
=

= 3 m
- 0 3 1 +

+
4 =

G +

,30d .
28/0 2 jj18
jsdodli Plo : Jsli ! S = [3 1) .
:64
bwj/jasS0gP)O j81 !

&
de 10 , S10 ,
Po oblich
tJ
: = - 0 , -1a

am" +
bw + c = 0

a b + + c = 0

aX +
bX + c = 0X = m2

X1 = mo - W = & va
Xz = mi N2-- Et -M

·
J
-
m +
17m2 -
16 = 0 · -d - IR 8

>
-

(2 +
17m -
16 = 0 1 = w2
D

X* 17X 16

·
-

+ - = 0

A =
178 47 1)) 16)
-

1 =
22r N = 1)

=1
Xe
b Xi Xn 16
-

= - =

-
2

X9 = X2
= X

X1
Ne
= m -

-W
Xa =
m
P
to --

Ny = -
1

113 -
. 8 di=

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