Question

f(x)=｛-cosπx,x＞0 f(x+1)+1,x＜=0,则f(4/3)+f(-4/3)的值等于?

Answer 1

f(4/3)+f(-4/3)

f(-4/3)=f(-4/3+1)+1

=f(-1/3)+1

= f(-1/3+1)+1

=f(2/3)+1

=-cos[π*(2/3)] +1

=1/2+1=3/2

f(4/3) =-cos[π*(4/3)]=1/2,

则f(4/3)+f(-4/3)=3/2+1/2=2.