设 f(x)= {sinπx(x

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设f(x)={sinπx(x设f(x)={sinπx(x设f(x)={sinπx(xf(x-1)+1(x≥0);g(x)={cosπx(xg(x-1)+1(x≥1/2)求g(1/4)+f(1/3)+g

设 f(x)= {sinπx(x
设 f(x)= {sinπx(x<0) f(x-1)+1 (x≥0)
设 f(x)= {sinπx(x<0)
f(x-1)+1 (x≥0) ;
g(x)={cosπx(x<1/2)
g(x-1)+1(x≥1/2)
求g(1/4)+f(1/3)+g(5/6+f(3/4) 的值.

设 f(x)= {sinπx(x
f(1/3)=f(-2/3)+1=-√3/2+1
f(3/4)=f(-1/4)+1=-√2/2+1
g(1/4)=√2/2
g(5/6)=g(-1/6)+1=√3/2+1
所以g(1/4)+f(1/3)+g(5/6)+f(3/4)=3.

分析：这是个分函数问题，f(1/3)=f(-2/3)+1=1-根号3/2；
同理：f(3/4)=1-根号2/2
g(1/4)=cos(π/4)=根号2/2
g(5/6)=g(-1/6)=1+根号3/2
所以和为3

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