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's a step-by-step guide to finding [tex]\( f(3) \)[/tex]:
1. Substitute [tex]\( x = 3 \)[/tex] into the function:
[tex]\[
f(3) = \left(\frac{1}{9}\right) \cdot (9^3)
\][/tex]
2. Calculate [tex]\( 9^3 \)[/tex]:
[tex]\[
9^3 = 9 \times 9 \times 9 = 729
\][/tex]
3. Multiply by [tex]\(\frac{1}{9}\)[/tex]:
[tex]\[
f(3) = \left(\frac{1}{9}\right) \cdot 729
\][/tex]
4. Simplify the multiplication:
[tex]\[
\frac{729}{9} = 81
\][/tex]
Thus, [tex]\( f(3) = 81 \)[/tex].
The correct answer is C. 81.
Here's a step-by-step guide to finding [tex]\( f(3) \)[/tex]:
1. Substitute [tex]\( x = 3 \)[/tex] into the function:
[tex]\[
f(3) = \left(\frac{1}{9}\right) \cdot (9^3)
\][/tex]
2. Calculate [tex]\( 9^3 \)[/tex]:
[tex]\[
9^3 = 9 \times 9 \times 9 = 729
\][/tex]
3. Multiply by [tex]\(\frac{1}{9}\)[/tex]:
[tex]\[
f(3) = \left(\frac{1}{9}\right) \cdot 729
\][/tex]
4. Simplify the multiplication:
[tex]\[
\frac{729}{9} = 81
\][/tex]
Thus, [tex]\( f(3) = 81 \)[/tex].
The correct answer is C. 81.
