The function fff is defined by f(x)=∣x−12∣+15 for x∈Rf(x) = |x - 12| + 15 \text{ for } x \in \mathbb{R}f(x)=∣x−12∣+15 for x∈R The function ggg is defined by g(x)=e2x+15g(x) = e^{2x} + 15g(x)=e2x+15 where ggg has its greatest possible domain.
Using set notation, state the range of fff.
State the domain of ggg.
The composite function hhh is given by h(x)=fg(x) for x∈domain of gh(x) = f g(x) \text{ for } x \in \text{domain of } gh(x)=fg(x) for x∈domain of g (i) Write down an expression for h(x)h(x)h(x) in terms of xxx. (ii) Determine if hhh has an inverse. Fully justify your answer.
