3.6: Logarithmic range, composite and derivative equal to inverse

0606/11/M/J/22 — Question 3 · 10 marks

A function ff is such that f(x)=ln⁡(2x+1)f(x) = \ln(2x + 1), for x>−12x > -\dfrac{1}{2}.
(a)
Write down the range of ff.
[1]
(b)
A function gg is such that g(x)=5x−7g(x) = 5x - 7, for x∈Rx \in \mathbb{R}.
Find the exact solution of the equation gf(x)=13gf(x) = 13.
[3]
(c)
Find the solution of the equation f′(x)=g−1(x)f'(x) = g^{-1}(x).
[6]