\(Suppose that $g(x)=f^{-1}(x)$. If $g(-15)=0$, $g(0)=3$, $g(3)=9$ and $g(9)=20$, what is $f(f(9))$?\)
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
Please help! Do not know hot to solve
\(\begin{array}{|rcl|rcl|} \hline g(x) &&& f(x)&=&g^{-1}(x) \\ \hline g(-15)&=&0 & f(0)&=&-15 \\ g(0)&=&3 & f(3) &=& 0 \\ g(3)&=&9 & f(9) &=& 3 \\ g(9)&=&20 & f(20) &=& 9 \\ \hline \end{array} \)
\(\mathbf{f(f(9))} = f(3) \mathbf{= 0} \)