We will have the following:
*First: We would determine the piecewise function that describes the graph.
Since we can see that the function increases by a factor of 2 and decreases by the same factor we would have:
[tex]f(x)=\begin{cases}2x\colon x\ge0\land x\le4 \\ \\ -2x+16\colon x>4\land\le8\end{cases}[/tex]
This is:
*Second: We calculate the inverse of the piecewise function:
[tex]f^{-1}(x)=\begin{cases}\frac{x}{2}\colon x\ge0\land x\le4 \\ \\ -\frac{x-16}{2}\colon x>4\land x\le8\end{cases}[/tex]
That is:
From this we can see that the inverse of that graph would in fact represent a function, a non-continuous function. [It will represent a function as long as it follows the parameters stablished in the first point]
