Question

已知函数f(x)=log2(4^x+1)+kx,(k∈R)是偶函数 求K的值

写过程

Answer 1

解：f(1)=log2^5+k
f(-1)=log2^(5/4)-k
∵函数f(x)=log2(4^x+1)+kx,(k∈R)是偶函数
∴f(1)=f(-1)
即log2^5+k=log2^(5/4)-k
2k=log2(5/4)-log2^5
=log2(1/4)
=-2
∴k=-1

Answer 2

f(x)=f(-x)
log2(4^x+1)+kx=log2[4^(-x)+1]-kx
log2{(4^x+1)/[4^(-x)+1]=-2kx
2^(-2kx)*[4^(-x)+1]=4^x+1
k=-1