<s>[INST] The figure below shows the graph of a function $f(x)$. How many solutions does the equation $f(f(x)) = 15$ have? From the graph we can find that, $f(-5)=f(-1)=f(9)=0$

 [/INST] We are to find the solutions for $f(f(x)) = 15$.
From the graph, $f(4) = 15$ and $f(12) = 15$.
The required solutions will be those values of $x$ for which $f(x) = 4$ and $f(x) = 12$.
From the graph, the value of function $f(x) = 4$ at four different values of $x$, namely $x = –8, 1, 7.5, 10$.
The value of the function $f(x) = 12$ at three different points, namely $x = 3.5, 5.25, 11.5$.
Hence, the given equation has 7 solutions.
</s>