Answer :
To find the value of [tex]\( f(3) \)[/tex] for the function [tex]\( f(x) = \left(\frac{1}{9}\right)\left(9^x\right) \)[/tex], follow these steps:
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 by [tex]\(\frac{1}{9}\)[/tex]:
[tex]\[
f(3) = \frac{1}{9} \times 729
\][/tex]
4. Simplify the expression:
[tex]\[
\frac{729}{9} = 81
\][/tex]
So, the value of [tex]\( f(3) \)[/tex] is [tex]\( 81 \)[/tex].
Thus, the correct answer is:
C. 81
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 by [tex]\(\frac{1}{9}\)[/tex]:
[tex]\[
f(3) = \frac{1}{9} \times 729
\][/tex]
4. Simplify the expression:
[tex]\[
\frac{729}{9} = 81
\][/tex]
So, the value of [tex]\( f(3) \)[/tex] is [tex]\( 81 \)[/tex].
Thus, the correct answer is:
C. 81
