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Suppose there are two functions \( f \) and \( g \), whose values are defined by the table below. Calculate \( f^{-1}(g(2)) \).

\begin{tabular}{|l|l|l|l|l|l|l|}
\hline
[tex]$x$[/tex] & 1 & 2 & 3 & 4 & [tex]$K$[/tex] & [tex]$Q$[/tex] \\
\hline
[tex]$f(x)$[/tex] & 12 & 3 & 1 & 2 & 4 & 7 \\
\hline
[tex]$g(x)$[/tex] & 11 & 2 & 4 & 1 & 8 & 7 \\
\hline
\end{tabular}

Sagot :

GinnyAnswer
To calculate \( f^{-1}(g(2)) \), we need to follow these steps:

1. Determine the value of \( g(2) \):
From the table given:
[tex]\[ g(2) = 2 \][/tex]

2. Find \( f^{-1}(2) \):
\( f^{-1}(2) \) means we need to find the value of \( x \) such that \( f(x) = 2 \). We look at the table of \( f(x) \):
[tex]\[ \begin{array}{|l|l|l|l|l|l|l|} \hline x & 1 & 2 & 3 & 4 & K & Q \\ \hline f(x) & 12 & 3 & 1 & 2 & 4 & 7 \\ \hline \end{array} \][/tex]
From the table, we see that \( f(4) = 2 \).

Hence, \( f^{-1}(2) = 4 \).

Therefore, \( f^{-1}(g(2)) = 4 \). The final result is:
[tex]\[ f^{-1}(g(2)) = 4 \][/tex]
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