1. The problem asks to describe a sequence of transformations that transforms the graph of $y = g^{-1}(x)$ to the graph of $y = f(x)$. 2. From part (b)(i), we know $g^{-1}(x) = 2^{x-1}$. The function $f(x) = 4^x = (2^2)^x = 2^{2x}$. 3. The graph of $y = g^{-1}(x) = 2^{x-1}$ is the graph of $y = 2^x$ shifted to the right by 1 unit. 4. The graph of $y = f(x) = 2^{2x}$ can be seen as a horizontal compression of $y = 2^x$ by a factor of $\frac{1}{2}$. 5. To transform $y = g^{-1}(x)$ to $y = f(x)$, first undo the right shift by 1 unit (shift left by 1), then apply a horizontal compression by a factor of $\frac{1}{2}$. 6. In summary, the sequence of transformations is: 1) Shift the graph of $y = g^{-1}(x)$ left by 1 unit to get $y = 2^x$. 2) Horizontally compress the graph by a factor of $\frac{1}{2}$ to get $y = 2^{2x} = 4^x = f(x)$.