درس الدوال - 2 ثانوي
درس الدوال - 2 ثانوي
66165 .935
--
&ij
f(y) =...
Site a
g
Re 503
8() C f(y E :
Df
f(04) 8(2)
=
:
: 0 -
C
88-7 :
fl =
20
f(0) =
⑧
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[
w+ Gw = 0
Df =
3 -
.
fis
w(w 6) + = 0 ·
2j
-69026j2 ji f(u) 2 m
LpWE SN O
= +
me
&
& (m) = -
E -
wa + Gm + 2 = 7
- w -
4 30 ·
di Fdjj
w+ 6 m 2 +7 5
+ = 0
wXH :
-
8
# + xm += 0
Mot-3 o
- m
3 add -
71
f(m) =
(v a)a + + 7 ·
3
S am
f(u) = m2 + a +
2wa +
7 ·
%16)90
jsli ! =
J ligf
S
: .
Sli) :
20
>
- = 6
fluf > f(u) jig me wa f(we) <flu) 08 n . My
3 3Y
-y
f(u) =
mi + 6m +
2
8h
A
f=9 de
J
-m
-3 jigs
-
f(x) = - 0 - (w + 3) -
=
=
( 3)a + = - 8 +7
=
(49) =
4 as
·
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
·
ji[t[6851 / jis
( + 2)27( a)s +
+
(a + 2) y (+ 2)a
7
=
=
·
Glitaljbl zjfl f 16
2
-4
-
f() = Pf (ato
=
:
/20 Ad/
Ay
(07)
↓
1
Commentaie
=
- o C -
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
+ 3 en
mu
J
.
2
1.
2 .
2 /a -
2 (b- 2
0 /C -
2 [b - 2
(25 :
>Jos] sintu) , coscus : Hobo-
a
&j/10 a: Dy
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
3)2( b) - = a + b2ab :
5 flu gla) Q = :
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
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) =
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] ,
f(x) g(z) + = m -
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
*
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 -
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) =
=
Du =
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 ·
= + (1/4
↑
( -) 4.51420.
·
·
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 ..
D
-
[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
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) -
(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 ·
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
⑧
-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 =
0 f(a) 0j81/feg /j
=
a adlj955
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
4 :
No
= wo am10 er =-
.r & 7 jiz .
3
No =
5
64) =
-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=