3.16: Composite with ln and inverse sketch data

0606/12/M/J/23 — Question 8 · 8 marks · Exponentials, Equations

Year bank also crops permutations Q7; this entry is the logarithmic function question.

It is given that f(x)=2ln⁡(3x−4)f(x) = 2\ln(3x - 4) for x>ax > a.
(a)
State the least possible value of aa.
[1]
(b)
Find an expression for f−1(x)f^{-1}(x).
[3]
(c)
It is given that g(x)=2x−3g(x) = 2x - 3. Solve fg(g(x))=4fg\bigl(g(x)\bigr) = 4.
[4]