Question

已知函数f(x)=cosπx. (x≦0) f(x-1)+1 (x＞0)

则f(4/3)+f(-4/3)=

Answer 1

f(-4／3)=cos(-4/3∏)=-1／2,f(4／3)=f(4/3-1)+1=f(1/3)+1=f(1/3-1)+1+1=f(-2/3)+2=cos(-2/3∏)+2=-1/2+2,故两者之和=1.