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