Answer :
To find [tex]\( f(3) \)[/tex] for the function [tex]\( f(x) = \left(\frac{1}{9}\right)\left(9^x\right) \)[/tex], we follow these steps:
1. Substitute [tex]\( x = 3 \)[/tex] into the function.
The function is defined as:
[tex]\[
f(x) = \left(\frac{1}{9}\right)\left(9^x\right)
\][/tex]
We're calculating [tex]\( f(3) \)[/tex], so substitute [tex]\( x \)[/tex] with 3:
[tex]\[
f(3) = \left(\frac{1}{9}\right)\left(9^3\right)
\][/tex]
2. Calculate [tex]\( 9^3 \)[/tex].
The expression [tex]\( 9^3 \)[/tex] is computed as:
[tex]\[
9^3 = 9 \times 9 \times 9 = 729
\][/tex]
3. Multiply [tex]\(\frac{1}{9}\)[/tex] by [tex]\( 729 \)[/tex].
Now, multiply the result from step 2 by [tex]\(\frac{1}{9}\)[/tex]:
[tex]\[
\left(\frac{1}{9}\right) \times 729 = \frac{729}{9} = 81
\][/tex]
Therefore, [tex]\( f(3) = 81 \)[/tex].
The correct answer is A. 81.
1. Substitute [tex]\( x = 3 \)[/tex] into the function.
The function is defined as:
[tex]\[
f(x) = \left(\frac{1}{9}\right)\left(9^x\right)
\][/tex]
We're calculating [tex]\( f(3) \)[/tex], so substitute [tex]\( x \)[/tex] with 3:
[tex]\[
f(3) = \left(\frac{1}{9}\right)\left(9^3\right)
\][/tex]
2. Calculate [tex]\( 9^3 \)[/tex].
The expression [tex]\( 9^3 \)[/tex] is computed as:
[tex]\[
9^3 = 9 \times 9 \times 9 = 729
\][/tex]
3. Multiply [tex]\(\frac{1}{9}\)[/tex] by [tex]\( 729 \)[/tex].
Now, multiply the result from step 2 by [tex]\(\frac{1}{9}\)[/tex]:
[tex]\[
\left(\frac{1}{9}\right) \times 729 = \frac{729}{9} = 81
\][/tex]
Therefore, [tex]\( f(3) = 81 \)[/tex].
The correct answer is A. 81.
