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Given the table with selected values of [tex]\( f(x) \)[/tex] and [tex]\( g(x) \)[/tex], evaluate [tex]\( f(g(4)) \)[/tex]:

[tex]\[
\begin{array}{|c|c|c|c|c|c|c|}
\hline
x & -3 & -2 & 1 & 4 & 6 & 9 \\
\hline
f(x) & 2 & 4 & 9 & 1 & -4 & -2 \\
\hline
g(x) & -6 & 1 & 4 & 6 & 9 & 3 \\
\hline
\end{array}
\][/tex]

A. [tex]\(-4\)[/tex]

B. [tex]\(-2\)[/tex]

C. 2

D. 9

Sagot :

GinnyAnswer
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]
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