Answer :
To solve the problem, we need to evaluate the function [tex]\( f(x) = \left(\frac{1}{9}\right)\left(9^x\right) \)[/tex] at [tex]\( x = 3 \)[/tex].
Here are the steps:
1. Substitute 3 for [tex]\( x \)[/tex] in the function:
We have [tex]\( f(3) = \left(\frac{1}{9}\right) \left(9^3\right) \)[/tex].
2. Calculate [tex]\( 9^3 \)[/tex]:
[tex]\( 9^3 \)[/tex] means multiplying 9 by itself three times:
[tex]\[
9^3 = 9 \times 9 \times 9 = 729
\][/tex]
3. Multiply by [tex]\( \frac{1}{9} \)[/tex]:
Now, multiply [tex]\( 729 \)[/tex] by [tex]\( \frac{1}{9} \)[/tex]:
[tex]\[
f(3) = \frac{1}{9} \times 729 = \frac{729}{9} = 81
\][/tex]
So, the value of [tex]\( f(3) \)[/tex] is 81.
Therefore, the correct answer is [tex]\( \boxed{81} \)[/tex].
Here are the steps:
1. Substitute 3 for [tex]\( x \)[/tex] in the function:
We have [tex]\( f(3) = \left(\frac{1}{9}\right) \left(9^3\right) \)[/tex].
2. Calculate [tex]\( 9^3 \)[/tex]:
[tex]\( 9^3 \)[/tex] means multiplying 9 by itself three times:
[tex]\[
9^3 = 9 \times 9 \times 9 = 729
\][/tex]
3. Multiply by [tex]\( \frac{1}{9} \)[/tex]:
Now, multiply [tex]\( 729 \)[/tex] by [tex]\( \frac{1}{9} \)[/tex]:
[tex]\[
f(3) = \frac{1}{9} \times 729 = \frac{729}{9} = 81
\][/tex]
So, the value of [tex]\( f(3) \)[/tex] is 81.
Therefore, the correct answer is [tex]\( \boxed{81} \)[/tex].
