Given the function f (x) = loga [(a ^ x) - 1], a is greater than 1 1. Find the domain of F (x); 2. Find the value of X that holds f (2x) = f ^ - 1 (x) | Math enthusiast | Mathematical art

Given the function f (x) = loga [(a ^ x) - 1], a is greater than 1 1. Find the domain of F (x); 2. Find the value of X that holds f (2x) = f ^ - 1 (x)

1. If a ^ X-1 > 0, then a ^ x > 1, then x > 0
2. If the inverse function of F = loga [a ^ x + 1] (which can be obtained by exchanging X and f (x)), then a ^ 2x-1 = a ^ x + 1, then a ^ x = 2 or - 1 (rounding), so x = loga2

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