To evaluate [tex]\( f(g(4)) \)[/tex] using the given table, follow these steps:
1. Identify the value of [tex]\( g(4) \)[/tex] using the [tex]\( g(x) \)[/tex] row.
2. Use the value found in step 1 as the input for [tex]\( f(x) \)[/tex] to find [tex]\( f(g(4)) \)[/tex].
Step-by-step solution:
1. From the table, find [tex]\( g(4) \)[/tex]:
[tex]\[
g(4) = 1
\][/tex]
2. Now, using [tex]\( g(4) = 1 \)[/tex] as the new input, find [tex]\( f(g(4)) \)[/tex]:
[tex]\[
f(g(4)) = f(1)
\][/tex]
3. From the table, find [tex]\( f(1) \)[/tex]:
[tex]\[
f(1) = 9
\][/tex]
Therefore, [tex]\( f(g(4)) = 9 \)[/tex].
So, the evaluated value of [tex]\( f(g(4)) \)[/tex] is:
[tex]\[
\boxed{9}
\][/tex]
