若函数f(x)=alog₂x+blog₃x+2(a,b∈R),f(1/2009)=4,则f(2009)=a.-4b.2c.0d.-2
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/27 18:07:58
![若函数f(x)=alog₂x+blog₃x+2(a,b∈R),f(1/2009)=4,则f(2009)=a.-4b.2c.0d.-2](/uploads/image/z/13350225-57-5.jpg?t=%E8%8B%A5%E5%87%BD%E6%95%B0f%EF%BC%88x%EF%BC%89%3Dalog%26%238322%3Bx%2Bblog%26%238323%3Bx%2B2%EF%BC%88a%2Cb%E2%88%88R%EF%BC%89%2Cf%EF%BC%881%2F2009%EF%BC%89%3D4%2C%E5%88%99f%EF%BC%882009%EF%BC%89%3Da.-4b.2c.0d.-2)
若函数f(x)=alog₂x+blog₃x+2(a,b∈R),f(1/2009)=4,则f(2009)=a.-4b.2c.0d.-2
若函数f(x)=alog₂x+blog₃x+2(a,b∈R),f(1/2009)=4,则f(2009)=
a.-4
b.2
c.0
d.-2
若函数f(x)=alog₂x+blog₃x+2(a,b∈R),f(1/2009)=4,则f(2009)=a.-4b.2c.0d.-2
f(x)=alog₂x+blog₃x+2
f(1/x)=alog₂(1/x)+blog₃(1/x)+2
= -alog₂x - blog₃x +2
设x=2009,那么
f(1/2009)= -alog₂2009- blog₃2009 +2 = 4
所以
f(2009) = alog₂2009+blog₃2009+2 = -2 + 2 =0
选c
c.0
alog₂x+blog₃x=g(x)
奇函数