已知f(x)=sinπx(x＜0)f(x-1)-1(x＞0)则f(-116)+f(116)的值为（）A．-1B．-2-3C．-2D．-3

Question

已知 f(x)=

sinπx(x＜0)

f(x-1)-1(x＞0)

则 f(-(11)/(6) )+f((11)/(6) ) 的值为（　　）

A．-1

B． -2- 3

C．-2

D．-3

Answer 1

∵ f(x)=

sinπx(x＜0)

f(x-1)-1(x＞0)

∴ f(-(11)/(6) ) =sin（- (11π)/(6) ）=-sin (π)/(6) =- (1)/(2)
f((11)/(6) ) = f((11)/(6) -1)-1 = f((5)/(6) )-1 = f((5)/(6) -1)-2 = f(-(1)/(6) )-2 =-sin (π)/(6) -2=- (5)/(2)
故 f(-(11)/(6) )+f((11)/(6) ) =-3
故选D