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Answer :
Sure, let's find [tex]\( f(2) \)[/tex] for the given function [tex]\( f(x) = 3^{(x+4)} \)[/tex].
1. Substitute [tex]\( x = 2 \)[/tex] into the function [tex]\( f(x) \)[/tex]:
[tex]\[ f(2) = 3^{(2+4)} \][/tex]
2. Simplify the expression in the exponent:
[tex]\[ 2 + 4 = 6 \][/tex]
So,
[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]
We can 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]
So,
[tex]\[ f(2) = 729 \][/tex]
Therefore, the correct answer is [tex]\( 729 \)[/tex].
1. Substitute [tex]\( x = 2 \)[/tex] into the function [tex]\( f(x) \)[/tex]:
[tex]\[ f(2) = 3^{(2+4)} \][/tex]
2. Simplify the expression in the exponent:
[tex]\[ 2 + 4 = 6 \][/tex]
So,
[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]
We can 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]
So,
[tex]\[ f(2) = 729 \][/tex]
Therefore, the correct answer is [tex]\( 729 \)[/tex].
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