已知函数f(x)=sin(π2-πx),(x≤0)-12x-12,(x>0),则f(f(12))的值是______.-数学

题目简介

已知函数f(x)=sin(π2-πx),(x≤0)-12x-12,(x>0),则f(f(12))的值是______.-数学

题目详情

已知函数f(x)=
sin(
π
2
-πx),(x≤0)
-
1
2
x-
1
2
,(x>0)
,则f(f(
1
2
))的值是______.
题型:填空题难度:中档来源:不详

答案

f(x)=
sin(class="stub"π
2
-πx),(x≤0)
-class="stub"1
2
x-class="stub"1
2
,(x>0)
=
cosπx,x≤0
-class="stub"1
2
x-class="stub"1
2
,x>0

f(class="stub"1
2
)=-class="stub"1
2
×class="stub"1
2
-class="stub"1
2
=-class="stub"3
4

f(f(class="stub"1
2
))
=f(-class="stub"3
4
)
=cos(-class="stub"3π
4
)
=cosclass="stub"3π
4
=-
2
2

故答案为:-
2
2

更多内容推荐