Answer :

To find [tex]\( f(2) \)[/tex] for the function [tex]\( f(x) = 3^{(x + 4)} \)[/tex], we need to substitute [tex]\( x = 2 \)[/tex] into the function and solve the expression.

Here are the steps:

1. Start with the function:
[tex]\[
f(x) = 3^{(x + 4)}
\][/tex]

2. Substitute [tex]\( x = 2 \)[/tex] into the function:
[tex]\[
f(2) = 3^{(2 + 4)}
\][/tex]

3. Simplify the exponent:
[tex]\[
2 + 4 = 6
\][/tex]

4. Now compute [tex]\( 3^6 \)[/tex]:
[tex]\[
3^6 = 3 \times 3 \times 3 \times 3 \times 3 \times 3
\][/tex]

5. Solving step by step:
- [tex]\( 3 \times 3 = 9 \)[/tex]
- [tex]\( 9 \times 3 = 27 \)[/tex]
- [tex]\( 27 \times 3 = 81 \)[/tex]
- [tex]\( 81 \times 3 = 243 \)[/tex]
- [tex]\( 243 \times 3 = 729 \)[/tex]

So, the value of [tex]\( f(2) \)[/tex] is [tex]\( 729 \)[/tex].

Therefore, the correct answer is [tex]\(\boxed{729}\)[/tex].

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