4. $$\begin{aligned} & f ( x ) = \mathrm { e } ^ { x } , x \in \mathbb { R } , x > 0
& g ( x ) = 2 x ^ { 3 } + 11 , x \in \mathbb { R } \end{aligned}$$ a) Find and simplify an expression for the composite function \(g f ( x )\).
b) State the domain and range of \(g f ( x )\).
c) Solve the equation $$g f ( x ) = 27$$ The equation \(g f ( x ) = k\), where \(k\) is a constant, has solutions.
d) State the range of the possible values of \(k\).
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