Answer :
To find [tex]\( f(3) \)[/tex] given the function [tex]\( f(x) = \left(\frac{1}{9}\right)\left(9^x\right) \)[/tex], we can follow these steps:
1. Substitute 3 into the function:
Start by substituting [tex]\( x = 3 \)[/tex] into the function. So, it becomes:
[tex]\[
f(3) = \left(\frac{1}{9}\right)\left(9^3\right)
\][/tex]
2. Calculate [tex]\( 9^3 \)[/tex]:
Compute [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]:
Now, multiply the result by [tex]\(\frac{1}{9}\)[/tex]:
[tex]\[
\left(\frac{1}{9}\right) \times 729 = \frac{729}{9}
\][/tex]
4. Simplify the fraction:
Divide 729 by 9 to simplify the expression:
[tex]\[
\frac{729}{9} = 81
\][/tex]
Therefore, [tex]\( f(3) = 81 \)[/tex].
The correct answer is D. 81.
1. Substitute 3 into the function:
Start by substituting [tex]\( x = 3 \)[/tex] into the function. So, it becomes:
[tex]\[
f(3) = \left(\frac{1}{9}\right)\left(9^3\right)
\][/tex]
2. Calculate [tex]\( 9^3 \)[/tex]:
Compute [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]:
Now, multiply the result by [tex]\(\frac{1}{9}\)[/tex]:
[tex]\[
\left(\frac{1}{9}\right) \times 729 = \frac{729}{9}
\][/tex]
4. Simplify the fraction:
Divide 729 by 9 to simplify the expression:
[tex]\[
\frac{729}{9} = 81
\][/tex]
Therefore, [tex]\( f(3) = 81 \)[/tex].
The correct answer is D. 81.
