- , - . . , , .
, , , , , , . , , , .
44. .
.
1) 2 .
2) .
, ?
, , . - {1, 3, 5, 7} {2, 6, 10, 14}, - (0,1,2, 3,4, 5} {5, 4, 3, 2, 1, 0}. ? , . . :
. X R , X R.
X .
f, g, h . f - , X, , X, f(x) = f(). ( ) f. f() X f.
X = {1, 3, 5, 7} - . {2,6,10,14}.
, , -, X, .. , , -, , X .
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, , . , = 2-3, = 2, = 3, - , , , , .
, , . , = 2-3, R, = 2-3, N. , = -5 -13, = -5 .
. , f(x) f(x). , = 2-3, R . = , - R , 2 ( = 2, ).
. = f(x) - X. , f(x) X.
, = 2-3, R, (. 1), = 2, R, - (. 2).
.1 .2
. , , 3, , [-2, 3], - {-2, -1,0, 1, 2, 3}.
.3
. , , , , . , . , 4 - , , . .
.4
, , , . - , t ?;
t ( ) | |||||||||
( ) | -3 | -7 | -5 | -3 |
. - , .
. f , .
. f , x1, x2 :
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1<2 f(x1)<f(2).
, , : (. 5).
. 5 .6
. f , 1, 2 :
1<2 f(x1)>f(2).
, , : (.6).
t - ( ), s - ( ), 4 /, s = 4t. t s, , s = 4t . .
. , =k, k - .
= k , = k , . , , . = k (k≠0). .
= k , . . : 2 , , ( ) = 2, .. k=2.
, .
1. = k .
2. , . , , .
, = 2, (1, 2), (. 7).
.7
3. k > 0 = k ; k < 0 - .
4. f - (1, 1), (2, 2) - , 2 ≠0 .
, f - , =k, 1 = k1, 2 = k2. 2≠0 k≠0, 2≠0. .
, : () () .
, , .
1. 8 16 . 48 , ?
. - , (.. , 1 ), , . - , , , - , 1 . , , - k, , = k = k, .. , , .
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:
1 : 2 :
1) 16:8 = 2 (.) 1) 48:16 = 3 ()
2) 48:2 = 24() 2) 8-3 = 24 ()
, , 2, , , = 2, , = 48.
: , , .
, .
t - ( ), v - ( /) 12 , v∙t = 20 v = .
t (t ≠ 0) v, , v = . .
. , = , k - .
, = , . , , . = k( ≠0). k .
= , . . : 12 : , - = 12, .. k=12.
, .
1. = , .
2. .
3. k > 0 1 - 3- = (. 8).
. 8 .9
< 0 2- 4- = (. 9).
4. f - (1, 1), (2, 2) - , .
, f - , = , . 1≠0, 2≠0, 3≠0,
, : () () .
, , .
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2. , 10 /, 6 . , 20 /?
. : , , , . , - , , . , - , - k, , = k = , .. , , .
:
1 : 2 :
1) 10-6 = 60 () 1) 20:10 = 2 ()
2) 60:20 = 3(4) 2) 6:2 = 3()
, , 60, , , = , , = 20.
: , .
, , , , .
3. , 2 . , , , ≤5. ? ?
. = 2 . =2 , ≤5, , 0, 1, 2, 3, 4, 5. . , 2, .. {0, 2, 4, 6, 8, 10}. , = 2 {0, 1, 2, 3, 4, 5} , 10. = 2.
. 10