Question

question
find $f^{-1}(g(13))$.
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$$\begin{tabular}{|c|c|c|} \\hline $x$ & $f(x)$ & $g(x)$ \\\\ \\hline 16 & 7 & 0 \\\\ \\hline 13 & $-16$ & 7 \\\\ \\hline $-8$ & 13 & $-20$ \\\\ \\hline $-20$ & $-15$ & 18 \\\\ \\hline 15 & $-11$ & 10 \\\\ \\hline $-15$ & 15 & $-13$ \\\\ \\hline $-2$ & 10 & 15 \\\\ \\hline \\end{tabular}$$

Explanation:

Step1: Find \( g(13) \)

Look at the table, when \( x = 13 \), \( g(x) = 7 \). So \( g(13)=7 \).

Step2: Find \( f^{-1}(7) \)

We need to find the \( x \) such that \( f(x)=7 \). From the table, when \( f(x) = 7 \), \( x = 16 \). So \( f^{-1}(7)=16 \).

Answer:

16