Please help! Do not know hot to solve

Suppose that   g(x) = f^-1(x) .  If   g(-15) = 0 ,  g(0) = 3 ,  g(3) = 9   and   g(9) = 20 ,  what is   f( f(9) ) ?

If     g(x) = f^-1(x)     then we can take  f  of both sides of the equation to get     f( g(x) )  =  x

Since  f( g(x) )  =  x  ,

f( g(3) )  =  3

                        And we know   g(3)  =  9   so we can substitute  9  in for  g(3)

f( 9 )  =  3

Again since  f( g(x) )  =  x  ,

f( g(0) )  =  0

                        And we know   g(0)  =  3   so we can substitute  3  in for  g(0)

f( 3 )  =  0

So we have found....

f( f(9) )   =  f( 3 )  =  0

https://web2.0calc.com/questions/help_31578#r3

 Please help! Do not know hot to solve

$\begin{array}{|rcl|rcl|} \hline g(x) &&& f(x)&=&g^{-1}(x) \\ \hline g(-15)&=&0 & f(0)&=&-15 \\ g(0)&=&3 & f(3) &=& 0 \\ g(3)&=&9 & f(9) &=& 3 \\ g(9)&=&20 & f(20) &=& 9 \\ \hline \end{array}$

$\mathbf{f(f(9))} = f(3) \mathbf{= 0}$