函数y=log2(4^x+1)-x的值域
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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,+∞)
= 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,+∞)
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