已知函数f(x)=sinπx,(x<0)f(x-1)-1(x>0),试求f(-116)+f(116)的值-数学

题目简介

已知函数f(x)=sinπx,(x<0)f(x-1)-1(x>0),试求f(-116)+f(116)的值-数学

题目详情

已知函数f(x)=
sinπx,(x<0)
f(x-1)-1(x>0)
,试求f(-
11
6
)+f(
11
6
)
的值
题型:解答题难度:中档来源:不详

答案

f(-class="stub"11
6
)=sin(-class="stub"11
6
π)=-sinclass="stub"11
6
π=-sin(2π-class="stub"π
6
)=sinclass="stub"π
6
=class="stub"1
2
f(class="stub"11
6
)=f(class="stub"5
6
)-1=f(-class="stub"1
6
)-2=sin(-class="stub"π
6
)-2=-class="stub"5
2

f(-class="stub"11
6
)+f(class="stub"11
6
)=class="stub"1
2
-class="stub"5
2
=-2

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