3.2: Exponential function inverse, sketch and composite

Find the domain of $f^{-1}$.

Solve $ff^{-1}(x) = \sqrt{5x - 4}$.

On the axes, sketch the graph of $y = f(x)$ and hence sketch the graph of $y = f^{-1}(x)$. Show clearly the positions of any points where your graphs meet the coordinate axes and the positions of any asymptotes.

The function $g$ is defined for $0 \leqslant x \leqslant 0.2$ by $g(x) = \dfrac{3}{1 - x}$.

Find and simplify an expression for $f^{-1}g(x)$.