The tables below show some inputs and outputs of functions [tex]\( f \)[/tex] and [tex]\( g \)[/tex].

\begin{tabular}{c|rrrrrr}
[tex]$x$[/tex] & -4 & -3 & -1 & 0 & 3 & 5 \\
\hline
[tex]$f(x)$[/tex] & 29 & 19 & 5 & 1 & 1 & 11
\end{tabular}

\begin{tabular}{c|rrrrrr}
[tex]$x$[/tex] & -5 & -1 & 0 & 1 & 4 & 8 \\
\hline
[tex]$g(x)$[/tex] & -10 & 2 & 5 & 8 & 17 & 29
\end{tabular}

Evaluate [tex]\( f(g(0)) \)[/tex]:

[tex]\[ f(g(0)) = \boxed{\phantom{a}} \][/tex]



Answer :

To solve [tex]\( f(g(0)) \)[/tex], let's go through the process step by step:

1. Evaluate [tex]\( g(0) \)[/tex]:
- From the table for function [tex]\( g \)[/tex], we look up the value of [tex]\( g \)[/tex] at [tex]\( x = 0 \)[/tex].
- According to the table, [tex]\( g(0) = 5 \)[/tex].

2. Evaluate [tex]\( f \)[/tex] at [tex]\( g(0) \)[/tex]:
- Now that we know [tex]\( g(0) = 5 \)[/tex], we next look up the value of [tex]\( f \)[/tex] at [tex]\( x = 5 \)[/tex].
- From the table for function [tex]\( f \)[/tex], we see that [tex]\( f(5) = 11 \)[/tex].

Thus, [tex]\( f(g(0)) = f(5) = 11 \)[/tex].

Therefore, the result is:
[tex]\[ f(g(0)) = 11 \][/tex]