f(x)=sin(3x+π\4)向左移m为偶函数,求m

f(x)=sin(3x+π\4)向左移m为偶函数,求m
f(x)=sin(3x+π\4)向左移m为偶函数,求m

f(x)=sin(3x+π\4)向左移m为偶函数,求m
左移后函数为
f(x)=sin(3(x+m)+π/4)=sin(3x+3m+π/4)
令3x+3m+π/4=π/2+kπ ,k为整数
则对称轴为:x =π/12-m+kπ/3
因为f(x) 为偶函数,所以 对称轴有一条是y轴,也即x=0
所以m=π/12+kπ/3