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