Answer :
To solve the problem, we need to find [tex]\( f(3) \)[/tex] for the function [tex]\( f(x) = \left(\frac{1}{9}\right)\left(9^x\right) \)[/tex].
Step-by-step Solution:
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].
So, substitute [tex]\( x = 3 \)[/tex] into the function to get:
[tex]\[
f(3) = \left(\frac{1}{9}\right)\left(9^3\right)
\][/tex]
2. Calculate [tex]\( 9^3 \)[/tex]:
We need to calculate [tex]\( 9^3 \)[/tex], which means multiplying 9 by itself three times:
[tex]\[
9^3 = 9 \times 9 \times 9 = 729
\][/tex]
3. Multiply by [tex]\(\frac{1}{9}\)[/tex]:
Now, multiply the result by [tex]\(\frac{1}{9}\)[/tex] as per the function:
[tex]\[
f(3) = \left(\frac{1}{9}\right) \times 729
\][/tex]
Simplifying this calculation gives:
[tex]\[
f(3) = \frac{729}{9} = 81
\][/tex]
Therefore, the value of [tex]\( f(3) \)[/tex] is 81. The correct answer is B. 81.
Step-by-step Solution:
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].
So, substitute [tex]\( x = 3 \)[/tex] into the function to get:
[tex]\[
f(3) = \left(\frac{1}{9}\right)\left(9^3\right)
\][/tex]
2. Calculate [tex]\( 9^3 \)[/tex]:
We need to calculate [tex]\( 9^3 \)[/tex], which means multiplying 9 by itself three times:
[tex]\[
9^3 = 9 \times 9 \times 9 = 729
\][/tex]
3. Multiply by [tex]\(\frac{1}{9}\)[/tex]:
Now, multiply the result by [tex]\(\frac{1}{9}\)[/tex] as per the function:
[tex]\[
f(3) = \left(\frac{1}{9}\right) \times 729
\][/tex]
Simplifying this calculation gives:
[tex]\[
f(3) = \frac{729}{9} = 81
\][/tex]
Therefore, the value of [tex]\( f(3) \)[/tex] is 81. The correct answer is B. 81.
