We have g(x) = 2 log (x - 3) + 1

Let y = g(x) = 2 log (x - 3) + 1

=> y - 1 = 2 log (x - 3)

=> (y - 1)/2 = log (x - 3)

taking the base of the log as 10

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We have g(x) = 2 log (x - 3) + 1

Let y = g(x) = 2 log (x - 3) + 1

=> y - 1 = 2 log (x - 3)

=> (y - 1)/2 = log (x - 3)

taking the base of the log as 10

=> 10^[(y - 1)/2] = x - 3

=> x = 10^[(y - 1)/2] + 3

interchange x and y

=> y = 10^[(x - 1)/2] + 3

Therefore the inverse function of g(x) is

**g^-1(x) = y = 10^[(x - 1)/2] + 3**