数学题求答案，有高中生帮一下吗？

Question

函数f(x)定义在整数集上，且满足f(n)={ n-3,n>=1000 f(f(n+5)),n<1000 ， 求f(100)

谁能用数学或者C++代码求解一下？

Answer 1

该回答引用自GPT-deepseek, 由博主 GISer Liu 编写：

好的，我们来逐步分析并解决这个问题。首先，我们需要理解函数 ( f(x) ) 的定义，并根据定义来求解 ( f(100) )。

分析问题

函数 ( f(x) ) 的定义如下：
[ f(n) = \begin{cases}
n - 3 & \text{如果 } n \geq 1000 \
f(f(n + 5)) & \text{如果 } n < 1000
\end{cases} ]

我们需要求 ( f(100) )。由于 ( 100 < 1000 )，我们使用第二个定义：
[ f(100) = f(f(105)) ]

接下来，我们需要求 ( f(105) )。由于 ( 105 < 1000 )，我们继续使用第二个定义：
[ f(105) = f(f(110)) ]

我们继续这个过程，直到我们找到一个 ( n \geq 1000 ) 的值。

逐步求解

1. ( f(100) = f(f(105)) )
2. ( f(105) = f(f(110)) )
3. ( f(110) = f(f(115)) )
4. ( f(115) = f(f(120)) )
5. ( f(120) = f(f(125)) )
6. ( f(125) = f(f(130)) )
7. ( f(130) = f(f(135)) )
8. ( f(135) = f(f(140)) )
9. ( f(140) = f(f(145)) )
10. ( f(145) = f(f(150)) )
11. ( f(150) = f(f(155)) )
12. ( f(155) = f(f(160)) )
13. ( f(160) = f(f(165)) )
14. ( f(165) = f(f(170)) )
15. ( f(170) = f(f(175)) )
16. ( f(175) = f(f(180)) )
17. ( f(180) = f(f(185)) )
18. ( f(185) = f(f(190)) )
19. ( f(190) = f(f(195)) )
20. ( f(195) = f(f(200)) )
21. ( f(200) = f(f(205)) )
22. ( f(205) = f(f(210)) )
23. ( f(210) = f(f(215)) )
24. ( f(215) = f(f(220)) )
25. ( f(220) = f(f(225)) )
26. ( f(225) = f(f(230)) )
27. ( f(230) = f(f(235)) )
28. ( f(235) = f(f(240)) )
29. ( f(240) = f(f(245)) )
30. ( f(245) = f(f(250)) )
31. ( f(250) = f(f(255)) )
32. ( f(255) = f(f(260)) )
33. ( f(260) = f(f(265)) )
34. ( f(265) = f(f(270)) )
35. ( f(270) = f(f(275)) )
36. ( f(275) = f(f(280)) )
37. ( f(280) = f(f(285)) )
38. ( f(285) = f(f(290)) )
39. ( f(290) = f(f(295)) )
40. ( f(295) = f(f(300)) )
41. ( f(300) = f(f(305)) )
42. ( f(305) = f(f(310)) )
43. ( f(310) = f(f(315)) )
44. ( f(315) = f(f(320)) )
45. ( f(320) = f(f(325)) )
46. ( f(325) = f(f(330)) )
47. ( f(330) = f(f(335)) )
48. ( f(335) = f(f(340)) )
49. ( f(340) = f(f(345)) )
50. ( f(345) = f(f(350)) )
51. ( f(350) = f(f(355)) )
52. ( f(355) = f(f(360)) )
53. ( f(360) = f(f(365)) )
54. ( f(365) = f(f(370)) )
55. ( f(370) = f(f(375)) )
56. ( f(375) = f(f(380)) )
57. ( f(380) = f(f(385)) )
58. ( f(385) = f(f(390)) )
59. ( f(390) = f(f(395)) )
60. ( f(395) = f(f(400)) )
61. ( f(400) = f(f(405)) )
62. ( f(405) = f(f(410)) )
63. ( f(410) = f(f(415)) )
64. ( f(415) = f(f(420)) )
65. ( f(420) = f(f(425)) )
66. ( f(425) = f(f(430)) )
67. ( f(430) = f(f(435)) )
68. ( f(435) = f(f(440)) )
69. ( f(440) = f(f(445)) )
70. ( f(445) = f(f(450)) )
71. ( f(450) = f(f(455)) )
72. ( f(455) = f(f(460)) )
73. ( f(460) = f(f(465)) )
74. ( f(465) = f(f(470)) )
75. ( f(470) = f(f(475)) )
76. ( f(475) = f(f(480)) )
77. ( f(480) = f(f(485)) )
78. ( f(485) = f(f(490)) )
79. ( f(490) = f(f(495)) )
80. ( f(495) = f(f(500)) )
81. ( f(500) = f(f(505)) )
82. ( f(505) = f(f(510)) )
83. ( f(510) = f(f(515)) )
84. ( f(515) = f(f(520)) )
85. ( f(520) = f(f(525)) )
86. ( f(525) = f(f(530)) )
87. ( f(530) = f(f(535)) )
88. ( f(535) = f(f(540)) )
89. ( f(540) = f(f(545)) )
90. ( f(545) = f(f(550)) )
91. ( f(550) = f(f(555)) )
92. ( f(555) = f(f(560)) )
93. ( f(560) = f(f(565)) )
94. ( f(565) = f(f(570)) )
95. ( f(570) = f(f(575)) )
96. ( f(575) = f(f(580)) )
97. ( f(580) = f(f(585)) )
98. ( f(585) = f(f(590)) )
99. ( f(590) = f(f(595)) )
100. ( f(595) = f(f(600)) )
101. ( f(600) = f(f(605)) )
102. ( f(605) = f(f(610)) )
103. ( f(610) = f(f(615)) )
104. ( f(615) = f(f(620)) )
105. ( f(620) = f(f(625)) )
106. ( f(625) = f(f(630)) )
107. ( f(630) = f(f(635)) )
108. ( f(635) = f(f(640)) )
109. ( f(640) = f(f(645)) )
110. ( f(645) = f(f(650)) )
111. ( f(650) = f(f(655)) )
112. ( f(655) = f(f(660)) )
113. ( f(660) = f(f(665)) )
114. ( f(665) = f(f(670)) )
115. ( f(670) = f(f(675)) )
116. ( f(675) = f(f(680)) )
117. ( f(680) = f(f(685)) )
118. ( f(685) = f(f(690)) )
119. ( f(690) = f(f(695)) )
120. ( f(695) = f(f(700)) )
121. ( f(700) = f(f(705)) )
122. ( f(705) = f(f(710)) )
123. ( f(710) = f(f(715)) )
124. ( f(715) = f(f(720)) )
125. ( f(720) = f(f(725)) )
126. ( f(725) = f(f(730)) )
127. ( f(730) = f(f(735)) )
128. ( f(735) = f(f(740)) )
129. ( f(740) = f(f(745)) )
130. ( f(745) = f(f(750)) )
131. ( f(750) = f(f(755)) )
132. ( f(755) = f(f(760)) )
133. ( f(760) = f(f(765)) )
134. ( f(765) = f(f(770)) )
135. ( f(770) = f(f(775)) )
136. ( f(775) = f(f(780)) )
137. ( f(780) = f(f(785)) )
138. ( f(785) = f(f(790)) )
139. ( f(790) = f(f(795)) )
140. ( f(795) = f(f(800)) )
141. ( f(800) = f(f(805)) )
142. ( f(805) = f(f(810)) )
143. ( f(810) = f(f(815)) )
144. ( f(815) = f(f(820)) )
145. ( f(820) = f(f(825)) )
146. ( f(825) = f(f(830)) )
147. ( f(830) = f(f(835)) )
148. ( f(835) = f(f(840)) )
149. ( f(840) = f(f(845)) )
150. ( f(845) = f(f(850)) )
151. ( f(850) = f(f(855)) )
152. ( f(855) = f(f(860)) )
153. ( f(860) = f(f(865)) )
154. ( f(865) = f(f(870)) )
155. ( f(870) = f(f(875)) )
156. ( f(875) = f(f(880)) )
157. ( f(880) = f(f(885)) )
158. ( f(885) = f(f(890)) )
159. ( f(890) = f(f(895)) )
160. ( f(895) = f(f(900)) )
161. ( f(900) = f(f(905)) )
162. ( f(905) = f(f(910)) )
163. ( f(910) = f(f(915)) )
164. ( f(915) = f(f(920)) )
165. ( f(920) = f(f(925)) )
166. ( f(925) = f(f(930)) )
167. ( f(930) = f(f(935)) )
168. ( f(935) = f(f(940)) )
169. ( f(940) = f(f(945)) )
170. ( f(945) = f(f(950)) )
171. ( f(950) = f(f(955)) )
172. ( f(955) = f(f(960)) )
173. ( f(960) = f(f(965)) )
174. ( f(965) = f(f(970)) )
175. ( f(970) = f(f(975)) )
176. ( f(975) = f(f(980)) )
177. ( f(980) = f(f(985)) )
178. ( f(985) = f(f(990)) )
179. ( f(990) = f(f(995)) )
180. ( f

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