Answer :
To find [tex]\( f(3) \)[/tex] for the function [tex]\( f(x) = \left(\frac{1}{9}\right)\left(9^x\right) \)[/tex], we simply need to substitute [tex]\( x = 3 \)[/tex] into the function and simplify.
Here's how it goes 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]\[
9^3 = 9 \times 9 \times 9 = 81 \times 9 = 729
\][/tex]
3. Multiply by [tex]\(\frac{1}{9}\)[/tex]:
[tex]\[
f(3) = \frac{1}{9} \times 729 = 81
\][/tex]
Therefore, the answer is [tex]\( f(3) = 81 \)[/tex].
So, the correct option is B. 81.
Here's how it goes 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]\[
9^3 = 9 \times 9 \times 9 = 81 \times 9 = 729
\][/tex]
3. Multiply by [tex]\(\frac{1}{9}\)[/tex]:
[tex]\[
f(3) = \frac{1}{9} \times 729 = 81
\][/tex]
Therefore, the answer is [tex]\( f(3) = 81 \)[/tex].
So, the correct option is B. 81.
