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Let g(x) = ax + b, where a, b are real numbers.
f(g(x)) = 3 (ax + b) + 5 = 3ax + 3b + 5
= (7x - 1)/3 = 7/3 x - 1/3
By correspondence, 3a = 7/3, so a = 7/9
3b + 5 = -1/3
3b = - 16/3
So b = -16/9
Thus g(x) = 7/9 x - 16/9
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