Answer :
To solve this problem, we need to find the value of the function [tex]\( f(x) = \left(\frac{1}{9}\right)\left(9^x\right) \)[/tex] when [tex]\( x = 3 \)[/tex].
Let's break it down step-by-step:
1. Substitute [tex]\( x = 3 \)[/tex] into the function:
[tex]\[
f(3) = \left(\frac{1}{9}\right)\left(9^3\right)
\][/tex]
2. Calculate [tex]\( 9^3 \)[/tex]:
[tex]\[
9^3 = 9 \times 9 \times 9 = 729
\][/tex]
3. Multiply [tex]\(\frac{1}{9}\)[/tex] by [tex]\( 729 \)[/tex]:
[tex]\[
\left(\frac{1}{9}\right) \times 729 = \frac{729}{9} = 81
\][/tex]
So, the value of [tex]\( f(3) \)[/tex] is 81.
Therefore, the correct answer is D. 81.
Let's break it down step-by-step:
1. Substitute [tex]\( x = 3 \)[/tex] into the function:
[tex]\[
f(3) = \left(\frac{1}{9}\right)\left(9^3\right)
\][/tex]
2. Calculate [tex]\( 9^3 \)[/tex]:
[tex]\[
9^3 = 9 \times 9 \times 9 = 729
\][/tex]
3. Multiply [tex]\(\frac{1}{9}\)[/tex] by [tex]\( 729 \)[/tex]:
[tex]\[
\left(\frac{1}{9}\right) \times 729 = \frac{729}{9} = 81
\][/tex]
So, the value of [tex]\( f(3) \)[/tex] is 81.
Therefore, the correct answer is D. 81.
