(a) The function \(f\) is defined by \(f(x)=\sqrt{1+x^2}\), for all real values of \(x\). The graph of \(y=f(x)\) is given.

(i) Explain, with reference to the graph, why \(f\) does not have an inverse.

(ii) Find \(f^2(x)\).

(b) The function \(g\) is defined, for \(x\gt k\), by \(g(x)=\sqrt{1+x^2}\), and \(g\) has an inverse.

(i) Write down a possible value for \(k\).

(ii) Find \(g^{-1}(x)\).

(c) The function \(h\) is defined, for all real values of \(x\), by \(h(x)=4e^x+2\). Sketch the graph of \(y=h(x)\). Hence, on the same axes, sketch the graph of \(y=h^{-1}(x)\). Give the coordinates of any points where your graphs meet the coordinate axes.