Question

数学抽象函数求值的问题已知f(x)=-cosπx,x>0,f(x+1)+1,x

Answer 1

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

=f(-1/3)+1

= 【f(-1/3+1)+1】+1

=f(2/3)+2

=-cos[π*(2/3)] +2

=1/2+2

=5/2

f(4/3) =-cos[π*(4/3)]=1/2,

则f(4/3)+f(-4/3)=5/2+1/2=3.