(a) It is given that \(g(x)=6x^4+5\) for all real \(x\).

(i) Explain why \(g\) is a function but does not have an inverse.

(ii) Find \(g^2(x)\) and state its domain.

It is given that \(h(x)=6x^4+5\) for \(x\leq k\).

(iii) State the greatest value of \(k\) such that \(h^{-1}\) exists.

(iv) For this value of \(k\), find \(h^{-1}(x)\).

(b) The function \(p\) is defined by \(p(x)=3e^x+2\) for all real \(x\).

(i) State the range of \(p\).

(ii) Sketch and label the graphs of \(y=p(x)\) and \(y=p^{-1}(x)\). State the coordinates of any points of intersection with the coordinate axes.

(iii) Hence explain why the equation \(p(x)=p^{-1}(x)\) has no solutions.