The diagram below shows the graph of the function $f(x)= ext{log}_2 x$, where $x>0$ - Scottish Highers Maths - Question 10 - 2016

To sketch the inverse function, $f^{-1}(x)$, we need to reflect the original graph of $f(x) = ext{log}_2 x$ across the line $y = x$. This means that for each point $(a, b)$ on the original graph, we will plot the point $(b, a)$ on the inverse graph.

1. Identify key points on the original curve. For instance, the point $(1, 0)$ on the original function corresponds to $(0, 1)$ for the inverse function.
2. The point $(4, 1)$ on the original function corresponds to $(1, 4)$ for the inverse function.

The graph of the inverse function will start from $(0, 1)$ and proceed upwards through $(1, 4)$, and continue to the right, maintaining the general shape of increasing curves, reflecting the behavior of the logarithmic function.