14ο λύκειο...
If you can't read please download the document
date post
11-Jan-2017Category
Education
view
7.777download
6
Embed Size (px)
Transcript of 14ο λύκειο...
14
14
1
1. :
) ( ) 1 1f x x x ) ( ) 5 5g x x x
) 1
( )3
xh x
x
)
2( )
2 15
xc x
x x
) ( ) 3 1d x x ) ( ) ln(1 ln )k x x
) ( ) 2 1l x x x ) 3( ) ln(2 )m x x
2. 2 2
2
1 , 5( )
ln( 1), 3
x xf x
x x x
. ,
f .
3.
x
2
e 1f(x)
3x 4 x 4. ,
f .
4. :
, 0 3
( ) 1, 1 0
2, 3 1
x x
f x x
x x
.
5. :
) ( )i f x x ) ( ) | |ii g x x ) ( ) | 1| 2iii h x x
,
6.
) 2 5 6
( )3
x xf x
x
) 2(x)= x +9- 6xf
) 13 3 3 2( ) x x xf x ) ( ) 1 2f x x
7. f , g g(x)=f 2(x)-2f(x)+x2+3 x , g .
8. f : : 3 2 2( ) 2 ( ) 5 ( ) x xf x f x f x e e , x . fC
xx.
9. f : R R 2
2
2 ( ) 3 ( ) 1( )
3 4
f x f xg x
x x
xR . Cg ' .
14
2
,
10.
2 2 4f x x x ,
2 2g x x x .
11. ( ) ( 2) ( 2)f x n x n x
x y=f(x)
ln5y .
12. f,g: , : xf(x) 1 g(x) e , x
f,g.
13. f(x) = x3+4x2+4x+1, g(x) = 2x2+5x +3. i) Cf Cg ; ii) Cf Cg
= 6..
14. f = g. f g R
f (x) = g(x).
) 3 2
( )x x
x
e xef x
xe
2
( ) 2xe
g xx
) 2
2
4( )
2 | |
xf x
x x
2( ) 1
| |g x
x
) 9
( )3
xf x
x
( ) 3g x x
) 3
1( )
1
xf x
x
3 2 3( ) 1g x x x
15. .
) 2f(x) ln(x 2) ln(2 x) g(x) ln(4 x )
)
x 1f(x) ln(x 1) ln(x 1) g(x) ln
x 1 ) 2f(x) 2ln(x 3) g x ln(x 3)
16. , ,
2x xf(x)
x 2
2x ( 1)x 2 3g(x)
x 1 .
17. f, g A :
f(x) f(x) g(x) 4 g(x) f(x) g(x) 4 8 x A . : f g .
18. f g x :
2 2 2 24 3 (x) 2 (x)g(x) g (x) 4x (x) ( )x f f f f x f g
14
3
19. 2 9
( )2
xf x
x
2
1( )
6
xg x
x x
.
: f g f g ,f
g.
20. f (x) 1x g(x) 6 x .
f+ g ,f- g ,f g , ,f g
g f.
21. 1, [0,2]
( ), (2,4]
x xf x
x x
2, [ 1,1]( )
2 4, (1,3]
x xg x
x x
.
: i) f g ii) f g
22. 1, [ 2,0]
( )2, (0,2]
xf x
x
0, [ 3, 1]( )
3, ( 1,1]
xg x
x
.
: i) f g ii) f g
23. fog , gof :
) (x)=x+3,x [0,2] f , g(x)=-x+2 [-2,2]
) 2
( )2
xf x
x
, ( )g x x
) ( )f x x , 2g(x)= 9-x
)2, 1
( ), 1
x xf x
x x
, g(x)=4x 2
) ( ) 2 f x x , 2g(x)= x 1
24. x
xxf
3)(
fof.
25. 2 3, 1 1
3 1, 1 10f x
x x
x x
2, 0 4
3, 4 7
x xg x
x x
.
fog.
14
4
26. f :
) (f og)(x) = x2-4x , x R g(x) = x+4
) (f og)(x) = 51 x , x -1 g(x) = -x5
) (fog)(x) =1
1
x
x
, x > -1 g(x) = ( 1)n x
27. g :
) 2f g x x x 1f x x
) xf g x e x x 1f x x
) 2 1f g x x lnx, 0f x x
) 8f g x x 1xf x e
28. f 0,1 .
:
) f x ) 4f x ) lnf x
29. f 5,8 .
g x f x f x
30. f(x) [1,4] ,
: ( ) ( 1) ( 3).h x f x f x
31. f : , : f x y f x f y ,
,x y :
) 0 0f ) f ) , ,f x y f x f y x y
) f
32. f : , : ( ) ( ) ( ) 1f xy f x f y xy
,x y . :
) ( )f ) 1 1
,( )
f xx f x
) ( )
1,( )
x f x xf x y
y f y y
33. f : :
) ( ) (2 23 )f x f x x ) 1 4
2 ( ) ,f x f xx x
.
14
5
34. f : :
) 2 ( ) 4 ( ) ,f x f x x x x ) 1 6
( ) 3 2 ,f x f x xx x
.
35. f : , : ( 1) ( )xf x e ef x ,
x .
) f ) f.
36. :f , 2 4( ) ,x f x x x x x
f.
37. :f , ln 1x
f x f xe
0x . ) f.
) fC .
) f.
38.
) ( ) 2 lnf x x ) ( ) 1 2f x x x ) 2( ) 1x xf x e e ) 1
xf x e
) 2( ) 2f x x x ) 2( ) 6 8f x x x )3
( )2
xf x
x
)
2
2( )
1
xf x
x
39. .
) 2
2
3 , 0( )
2 , 0xx x x
f xx x
)
2 3 0( )
1xx x
f xe x
40. f, g R, (
).
i) gof .
ii) fof gog.
iii) f (x) = ln [ln(x)], x > 1.
41. f . : i) -f
ii) kf k>0 k 0 f2
14
6
42. f : : 1 2 1 21
( ) ( )2
f x f x x x
1 2,x x 1 2x x . :
) 2
xg x f x .
) 2
xg x f x .
43. f 0, :
f xf x e x 0,x . f .
44. f
: 22
f xe x x ,0x .
45. : 0,f
: 2ln 4 1f x x x 2,x .
46. ) ( ) xf x x e
(0,)
) , 0, :
e e .
47. ) ( ) ln xf x x e
0,
) x>3 : 3 ln 3 ln3
xe .
48. ( ) xf x x , x , 0,1 .
) f .
) 3 3x x x x 0,1x
49. :f 3f x f x x x .
) f .
) 3 3 2f x f x
50. :f
3 3 22 2 5 1f x f x x x x x .
) f
14
7
) 3 1 1f x f x .
51. :f 3 3 3f x f x x
x .
) f
) 1 1f 3 0f . ) :
i. 2 2f f x f f x ii. 0f x iii. 1f x iv. 2 4 0f f x
52. 3( ) 5 1f x x x , x .
) f
) ( ) 7f f x .
53. ( ) lnxf x x , x >0 0,1 .
) f 0,
) : 2 2 2 24 9 ln( 4) ln( 9)x x x x x x
54. :f .
2 1fof x x fof x
55. 2 2 lnf x x x .
) ) f
.
) 0f x .
) 0f x .
56. f R
( ) ( ) ( )f x f y f xy x,yR.
(3 4) ( 2) (6 4) (2 1)f x f x f x f x .
57. f ( (3 7 0) )f x f x
x . A f
) f(x)=0 ) 2 0( )3f x
58. :
) 2( ) 2 3f x x x ) 2( ) 4 5f x x x
) 6 3( ) 4 3f x x x ) 2( ) 2 2x xf x e e
14
8
59. : 2y x
.
60. 2( ) 2f x x x , , x . , f
2 .
1-1
1 - 1
61. 1-1 :
) 2
(x)1
xf
x
) (x) 2f x )
3(x) 3x 2x 1f
) 2
2(x)
4
xf
x
)
2(x)
1
xf
x
) 2(x) xf e x
) 3
(x) xf e
) 2
(x) ln2
xf
x
62. 1-1 :
) ( ) 1f x x )3( ) 2 3 2f x x x ) ( ) 2xf x e x
) 4( ) 5f x x ) 23
2
xf x
x
1-1
63. ) A f : g : 1-1 , g f 1-1.
) f 1-1 (x)=[f(x)]3+2f(x)-3 1-1
64. :f : ( ) ( ) 2f f f x f f x x
x .
i) f .
ii) fC .
65. :f : 3( ) 4 ( ) 2 3f x f x x
x . :
) f 1-1 , ii) fC 1,1A .
1 - 1
66. A f : f(f(x))+f3(x)=2x+3 , x . ) f 1-1 ) f(2x3+x)=f(4-x)
14
9
67. f : R R
