F (x) = LG (1 + 2 ^ x + 4 ^ XA) / 3, where a ∈ R, if f (x) is meaningful when x ∈ (- infinity, 1], find the value range of A

F (x) = LG (1 + 2 ^ x + 4 ^ XA) / 3, where a ∈ R, if f (x) is meaningful when x ∈ (- infinity, 1], find the value range of A

The problem is equivalent to 1 + 2 ^ x + 4 ^ XA > 0 when x ∈ (- ∞, 1]
a>-[2^(-x)]^2-2^(-x)=-[2^(-x)+1/2]^2+1/4
x∈﹙－∞,1],2^(-x)∈[1/2,+∞)
So the maximum value on the right is - 1 + 1 / 4 = - 3 / 4
a>-3/4

Elden Ring Premiere

RELATED INFORMATIONS