1.17: Logarithmic inverse and composite equation

0606/13/O/N/20 — Question 3 · 7 marks

(a)(i)
It is given that f(x)=4ln⁡(2x−1)f(x) = 4\ln(2x - 1).
Write down the largest possible domain for the function ff.
[1]
(a)(ii)
Find f−1(x)f^{-1}(x) and its domain.
[3]
(b)
It is given that g(x)=x+5g(x) = x + 5 for x∈Rx \in \mathbb{R} and h(x)=2x−3h(x) = \sqrt{2x - 3} for x⩾32x \geqslant \tfrac{3}{2}.
Solve gh(x)=7gh(x) = 7.
[3]