Question

函数y=log2(4^x+1)-x的值域

Answer 1

y = log2(4^x+1)-x

= log2(4^x+1) - x log2 (2)

= log2(4^x+1) - log2 (2^x)

= log2{(4^x+1) /2^x}

= log2{(4^x/2^x +1/2^x}

= log2{ 2^x +1/2^x}

2x＞0,1/2^x＞0

2^x +1/2^x = (√2^x - 1/√2^x)^2 +2 ≥ 2

log2{ 2^x +1/2^x} ≥1

值域【1,+∞）