3.11: Quadratic and exponential: composite and inverses

0606/21/O/N/23 — Question 9 · 7 marks

The functions ff and gg are defined as follows, for all real values of xx.
f(x)=2x2−1f(x) = 2x^{2} - 1g(x)=ex+1g(x) = \mathrm{e}^{x} + 1
(a)
Solve the equation fg(x)=8fg(x) = 8.
[3]
(b)
For each of the functions ff and gg, either explain why the inverse function does not exist or find the inverse function, stating its domain.
[4]