According to the table, [tex]f(x) = 13[/tex] when [tex]x = 5[/tex]. This means
[tex]f(5)=13\implies f^{-1}(13) = 5[/tex]
From the table we also see that [tex]f(x)=5[/tex] when [tex]x=-9[/tex], so
[tex]f(-9)=5\implies f^{-1}(5)=-9[/tex]
So we have
[tex]f^{-1}\left(f^{-1}(13)\right) = f^{-1}(5)=-9[/tex]
On the other hand, the table shows [tex]f(x)=8[/tex] when [tex]x=-13[/tex], or
[tex]f(-13)=8\implies f^{-1}(8)=-13[/tex]
so the given equation is not true.
