Answer :
To solve the given problem, we need to evaluate the function [tex]\( f(x) = \left(\frac{1}{9}\right)\left(9^x\right) \)[/tex] at [tex]\( x = 3 \)[/tex].
Here’s how we do it step-by-step:
1. Substitute [tex]\( x = 3 \)[/tex] into the function.
The function is:
[tex]\[
f(x) = \left(\frac{1}{9}\right)\left(9^x\right)
\][/tex]
Plug [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]\[
f(3) = \left(\frac{1}{9}\right) \times 729
\][/tex]
4. Calculate the result.
[tex]\[
\left(\frac{1}{9}\right) \times 729 = \frac{729}{9} = 81
\][/tex]
Thus, the value of [tex]\( f(3) \)[/tex] is [tex]\( 81 \)[/tex].
The correct answer is [tex]\( \boxed{81} \)[/tex].
Here’s how we do it step-by-step:
1. Substitute [tex]\( x = 3 \)[/tex] into the function.
The function is:
[tex]\[
f(x) = \left(\frac{1}{9}\right)\left(9^x\right)
\][/tex]
Plug [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]\[
f(3) = \left(\frac{1}{9}\right) \times 729
\][/tex]
4. Calculate the result.
[tex]\[
\left(\frac{1}{9}\right) \times 729 = \frac{729}{9} = 81
\][/tex]
Thus, the value of [tex]\( f(3) \)[/tex] is [tex]\( 81 \)[/tex].
The correct answer is [tex]\( \boxed{81} \)[/tex].
