3.35: Composite fg and gg with ln

0606/21/O/N/22 — Question 9 · 10 marks · Exponentials, Equations

The functions f(x)f(x) and g(x)g(x) are defined for x>−23x > -\dfrac{2}{3} by f(x)=x2+1f(x) = x^{2} + 1 and g(x)=ln⁡(3x+2)g(x) = \ln(3x + 2).
(a)
Find fg(x)fg(x).
[1]
(b)
Solve the equation fg(x)=5fg(x) = 5, giving your answer in exact form.
[3]
(c)
Solve the equation gg(x)=1gg(x) = 1.
[6]