3.3: Exponential inverse, sketch and composite equation

Write down the range of $f$.

Find an expression for $f^{-1}$.

On the axes, sketch the graphs of $y = f(x)$ and $y = f^{-1}(x)$, stating the coordinates of the points where the curves meet the coordinate axes. State the equations of any asymptotes. Label your curves.

A function $g$ is such that $g(x) = x^{\frac{3}{2}} + 4$, $x \geqslant 0$.

Find the exact solution of the equation $gf(x) = 12$.