Answer :
To find [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 [tex]\(\frac{1}{9}\)[/tex] by 729.
[tex]\[
\left(\frac{1}{9}\right) \times 729 = \frac{729}{9}
\][/tex]
4. Divide 729 by 9.
[tex]\[
\frac{729}{9} = 81
\][/tex]
Thus, the value of [tex]\( f(3) \)[/tex] is [tex]\( 81 \)[/tex].
So the correct answer is:
A. 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 [tex]\(\frac{1}{9}\)[/tex] by 729.
[tex]\[
\left(\frac{1}{9}\right) \times 729 = \frac{729}{9}
\][/tex]
4. Divide 729 by 9.
[tex]\[
\frac{729}{9} = 81
\][/tex]
Thus, the value of [tex]\( f(3) \)[/tex] is [tex]\( 81 \)[/tex].
So the correct answer is:
A. 81
