Question

F^-1 (f^-1 (13))=f^-1 (8)​

Answer 1

According to the table, $f(x) = 13$ when $x = 5$. This means

$f(5)=13\implies f^{-1}(13) = 5$

From the table we also see that $f(x)=5$ when $x=-9$, so

$f(-9)=5\implies f^{-1}(5)=-9$

So we have

$f^{-1}\left(f^{-1}(13)\right) = f^{-1}(5)=-9$

On the other hand, the table shows $f(x)=8$ when $x=-13$, or

$f(-13)=8\implies f^{-1}(8)=-13$

so the given equation is not true.