Page 51 - الرياضيات المتقدمة كتاب الطالب للصف 11 الفصل 1

b Gb ^ Æar© {6 1.b d?Wb ç 2;N x- 'b X?cb f Ÿ .[ gb zB y2b

,1Vfa yb Y U1Ne
P ±Ò c ¯ P ±Ò ] ±»C< R ± ¤Ð­ C Õ 7 C F:94 »P0: ±

one-one
–œ — ½ § “½’ ¹ Э F:9 ±º¯ “› EÛ ±¹ ´C R P Ú b R C4 ± û0 ±
P ±Ò c ¯ ¹ Û P4
.(ž’ ¹ P Ò? ˜³C24 E; C ± ³P b ±
many-one
¹P4 c ¯ P ±Ò –› • ½œ § “½’¹ Э F:9 ±º¯ “œ ˜E Û R EÛ ±¹ P Ú b R C4 ± û0 ±
P Ò? –½ — › § “½’ à E; C ± ³P b ±
one-many
˜“½’ “à ¹’
domain EÛ ±P ± ÎC

range EÛ ±P ± ÓP –ž • ½Ÿ § “½’ ¹ F C ±º¯ “ E= 84 ± EÛ ±P ± P Ú b R C4 ± û0 ±
›-
˜“½’ ¹ P Ò? ˜E2= EÛ ±P E; C ± ³P b ±
E Û R: ± EÛ ±P ±
œ

composite function d Ÿ • ½›œ - ½œ D ± “ž ˜ZØ R: ± c ¯ ^ Ú :8Ù R/ Ô¹C ± û0 ±
œ
E= 84 ± EÛ ±P ± ˜Ê • “² • ½’­ ³»bj c ÒM± ³P b ±
inverse function G9 : ± ³»bj P Ò­ “Ÿ ´ b P b Z C ± û0 ±

C< 6; E= 84 ± EÛ ±P ±
R: M± X ± Îb ½C84 „C ˜ÎC8 ­ ³P4 E= P; E; C ± ³P b ±
self-inverse function
˜X7;: ±
ÒÍ

¦ † ` q-a 40-i . fa
C< Ûαҹ ³»bj d E R ± ´±»C 4 ± R= 6 E=6= R C4 ± û0 ± d F:Û94 Э \
˜E2= ± E= 84 ± ÛαÒP ±Ò E2= ± ÛαÒP ± D= R ¹C ¯ E=6= Ò –´C R Ò ´ P

¤^ –Ûαҹ ³»bj d C<9= : `8: d ± E= b= ± û ±b: ± ` R= 8 ± P b

˜` S ± »ÒR Z ÑP R Ò –` C ²ÒR/ ³»±R E »¹ `= E 4 ± y
˜C R= «C; ­ ³»C= E9 c9 E27 ÃC6 »± ^Û : d ± E 4 ± y

ÌR5 : ± ` S ±Ò –«C: ± »b ;j ` C< 9 P; E R d «C: ± ÃC6 »± ^Û : d ± E 4 ± y

˜] Q
˜C E R «P P4 R C8 d ± C R= 8 ± ¹P ^ : d ± E 4 ± y

Îb2 ± –³»±R ± E »¹Ò ` S ± ¤`= C=7 Ò­ `= =: `= ´C 4 ± c9 E9 ­ d ] º ^
Û
R==5 ± c9 C: P ­ d R==5 ± R @ û= Ò –` S ±Ò C R= 8 ± ¹P –` S ±Ò \:4 ± –E C : ±Ò
´C4 b ÏC=7 ± c9 E C;: ± ÛαÒP ± ϱP C û ±b: ± ÑQ ^= : C P C ˜R Š± d
¹P ¼ÒC = ÌR5 : ± ` S ± C ¤ÎC : ± ^= c9 –E= b= ± ³C= ± ` û ±b: \Û94

©C R= 8 `= E : ± C R= 8 ±
˜C<j±b Ò ÛαÒP9 CÕ7:4Ù CÕ:< d; Ëb –³P Øb ± ÑQ d
Û