Question

已知函数f(x)=log(4,(4^x+1)) -(1/2)x是偶函数,若方程f(x)-m=0有解,求实数m的取值范围?

Answer 1

f(x)-m=0转化为m=f(x)偶函数,看x≥0即可

m=f(x)=log4 (4^x+1)-log4 4^(1/2)x=log4 [(4^x+1)/(2×4^x)]

(4^x+1)/(2×4^x)=1/2+1/(2×4^x) x≥0时0