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The problem provided in the image is as follows:

**Given:**

\( f(x) = \ln(x - 1) + \ln 4 \), for \( x > 1 \).

**Tasks:**

a) Find \( f'(x) \).  
   Let \( g(x) = e^{f(x)} \) for \( x \in \mathbb{R} \).

b) Find \( g(f^{-1}(x)) \), giving your answer in the form \( ax + b \), where \( a, b \in \mathbb{Z}

Let f(x) = ln(x - 1) + ln 4, for x > 1. Find f'(x) and let g(x) = e^{f(x)} for x in R. Find g(f^{-1}(x)), giving your answer in the form ax + b, where a, b are integers. Also, find the domain and range of g∘f.

This problem explores the derivative of a logarithmic function and evaluates the composition of a function and its inverse. It uses key calculus concepts such as logarithmic differentiation and properties of inverse functions. Ideal for students in undergraduate calculus courses.

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