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1.今年元旦是星期日,试问今年元旦后的第1984~(1984)天是星期几。解:∵1984~(1984)=(283×7+3)~(1984) =7m+3~(1984),m∈N。而 3~6≡1(mod7),3~(1984)=3~4×3~(6×330) 3~4≡4(mod7),∴1984~(1984)≡4 (mod7)。答:今年元旦后的第1984~(1984)天是丛期四。 2.若f(x+1)=|x-1|,求f(1984)。解:令 x+1=1984,则x-1=1982, ∴ f(1984)=1982。 3.已知 f(x)=3x+1,g(x)=2x-1,h(g〔f(x)〕)=f(x)。求h(1984)。解:∵ f(y)=3y+1, ∴ g〔f(y)〕=2(3y+1)-1=6y+1, 故h(6y+1)=3y+1。令6y+1=1984,
1. New Year’s Day this year is Sunday. What is the day of the week 1984~(1984) after New Year’s Day this year? Solution: 1984~(1984)=(283×7+3)~(1984)=7m+3~(1984), m∈N. And 3~6≡1(mod7), 3~(1984)=3~4×3~(6×330) 3~4≡4(mod7), and 1984~(1984)≡4(mod7). A: The 1984-(1984) days after the New Year’s Day this year is the Fourth Cluster. 2. If f(x+1)=|x-1|, find f(1984). Solution: Let x+1=1984, then x-1=1982, ∴f(1984)=1982. 3. It is known that f(x)=3x+1, g(x)=2x-1, h(g[f(x)])=f(x). Seek h (1984). Solution: ∵ f(y)=3y+1, ∴ g[f(y)]=2(3y+1)-1=6y+1, so h(6y+1)=3y+1. Order 6y+1=1984,