Answer :
To find [tex]\( f(2) \)[/tex] for the function [tex]\( f(x) = 3^{(x+4)} \)[/tex], you need to substitute [tex]\( x = 2 \)[/tex] into the function.
Here's how to do it step-by-step:
1. Substitute [tex]\( x = 2 \)[/tex]:
[tex]\[
f(2) = 3^{(2+4)}
\][/tex]
2. Simplify the exponent:
[tex]\[
2 + 4 = 6
\][/tex]
So the expression becomes:
[tex]\[
f(2) = 3^6
\][/tex]
3. Calculate [tex]\( 3^6 \)[/tex]:
[tex]\[
3^6 = 3 \times 3 \times 3 \times 3 \times 3 \times 3
\][/tex]
Break it down 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]
Therefore, the value of [tex]\( f(2) \)[/tex] is [tex]\( 729 \)[/tex].
So, the correct answer is [tex]\( \boxed{729} \)[/tex].
Here's how to do it step-by-step:
1. Substitute [tex]\( x = 2 \)[/tex]:
[tex]\[
f(2) = 3^{(2+4)}
\][/tex]
2. Simplify the exponent:
[tex]\[
2 + 4 = 6
\][/tex]
So the expression becomes:
[tex]\[
f(2) = 3^6
\][/tex]
3. Calculate [tex]\( 3^6 \)[/tex]:
[tex]\[
3^6 = 3 \times 3 \times 3 \times 3 \times 3 \times 3
\][/tex]
Break it down 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]
Therefore, the value of [tex]\( f(2) \)[/tex] is [tex]\( 729 \)[/tex].
So, the correct answer is [tex]\( \boxed{729} \)[/tex].
