4.01: Quadratic sketch and exponential inverse

On the axes, sketch the graph of \(y=x^2-2x-3\). State the intercepts with the coordinate axes.

The function \(g\) is defined by \(g(x)=4\mathrm{e}^{x-2}-1\) for all real \(x\). Find an expression for \(g^{-1}(x)\).