Question

设f（x）={sinπx x＜0,f（x-1）+1 （x≥0） }和

Answer 1

g(1/4)=cos(1/4)π =2分之根号2

f(1/3)=sin(-2/3)π +1=-sin(2/3)π +1=1-2分之根号3

g(5/6)=g(5/6-1)+1=g(-1/6)π +1=g(1/6)π +1=cos(1/6)π +1=1+2分之根号3

f(3/4)=f(-1/3)π +1=sin(-1/3)π +1=-sin(1/3)π +1=1-2分之根号2

所以,g（1/4）+f（1/3）+g（5/6）+f（3/4）=2分之根号2+1-2分之根号3+1+2分之根号3+1-2分之根号2=2