Answer :
To find [tex]\( f(3) \)[/tex] for the function [tex]\( f(x) = \left(\frac{1}{9}\right)\left(9^x\right) \)[/tex], we'll follow these steps:
1. Substitute 3 for [tex]\( x \)[/tex]:
We need to evaluate the function at [tex]\( x = 3 \)[/tex]. So, we substitute 3 into the function:
[tex]\[
f(3) = \left(\frac{1}{9}\right)\left(9^3\right)
\][/tex]
2. Calculate [tex]\( 9^3 \)[/tex]:
Calculate the value of [tex]\( 9^3 \)[/tex] (9 raised to the power of 3):
[tex]\[
9^3 = 9 \times 9 \times 9 = 81 \times 9 = 729
\][/tex]
3. Multiply by [tex]\(\frac{1}{9}\)[/tex]:
Now, multiply [tex]\( 729 \)[/tex] by [tex]\(\frac{1}{9}\)[/tex]:
[tex]\[
\left(\frac{1}{9}\right) \times 729 = \frac{729}{9} = 81
\][/tex]
Therefore, the value of [tex]\( f(3) \)[/tex] is 81.
The correct answer is:
A. 81
1. Substitute 3 for [tex]\( x \)[/tex]:
We need to evaluate the function at [tex]\( x = 3 \)[/tex]. So, we substitute 3 into the function:
[tex]\[
f(3) = \left(\frac{1}{9}\right)\left(9^3\right)
\][/tex]
2. Calculate [tex]\( 9^3 \)[/tex]:
Calculate the value of [tex]\( 9^3 \)[/tex] (9 raised to the power of 3):
[tex]\[
9^3 = 9 \times 9 \times 9 = 81 \times 9 = 729
\][/tex]
3. Multiply by [tex]\(\frac{1}{9}\)[/tex]:
Now, multiply [tex]\( 729 \)[/tex] by [tex]\(\frac{1}{9}\)[/tex]:
[tex]\[
\left(\frac{1}{9}\right) \times 729 = \frac{729}{9} = 81
\][/tex]
Therefore, the value of [tex]\( f(3) \)[/tex] is 81.
The correct answer is:
A. 81
