Answer
(a) $ x\in(3,\infty)$
(b) $ y\in(-\infty,\infty)$
Work Step by Step
Function: $ y=\ln(x-3)+1$
(a) Domain: $ x-3\gt0$, $ x\in(3,\infty)$
(b) Range: $ y\in(-\infty,\infty)$
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