Answer :
To solve the problem, we need to evaluate the function [tex]\( f(x) = \left(\frac{1}{9}\right)\left(9^x\right) \)[/tex] for [tex]\( x = 3 \)[/tex].
Step-by-step solution:
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]\[
f(3) = \left(\frac{1}{9}\right) \times 729 = \frac{729}{9}
\][/tex]
4. Perform the division:
[tex]\[
\frac{729}{9} = 81
\][/tex]
Therefore, the value of [tex]\( f(3) \)[/tex] is 81. So, the correct answer is C. 81.
Step-by-step solution:
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]\[
f(3) = \left(\frac{1}{9}\right) \times 729 = \frac{729}{9}
\][/tex]
4. Perform the division:
[tex]\[
\frac{729}{9} = 81
\][/tex]
Therefore, the value of [tex]\( f(3) \)[/tex] is 81. So, the correct answer is C. 81.
