Answer :
To find [tex]\( f(3) \)[/tex] for the function [tex]\( f(x) = \left(\frac{1}{9}\right)\left(9^x\right) \)[/tex], we need to follow these steps:
1. Substitute the given value of [tex]\( x \)[/tex] into the function.
We are looking for [tex]\( f(3) \)[/tex], so we substitute [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].
To do this, multiply 9 by itself three times:
[tex]\[
9^3 = 9 \times 9 \times 9 = 729
\][/tex]
3. Multiply the result by [tex]\(\frac{1}{9}\)[/tex].
Now, substitute [tex]\( 9^3 = 729 \)[/tex] back into the equation:
[tex]\[
f(3) = \left(\frac{1}{9}\right) \times 729
\][/tex]
4. Perform the multiplication.
Divide 729 by 9 since multiplying by [tex]\(\frac{1}{9}\)[/tex] is the same as dividing by 9:
[tex]\[
\frac{729}{9} = 81
\][/tex]
Therefore, [tex]\( f(3) = 81 \)[/tex].
The correct option is B. 81.
1. Substitute the given value of [tex]\( x \)[/tex] into the function.
We are looking for [tex]\( f(3) \)[/tex], so we substitute [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].
To do this, multiply 9 by itself three times:
[tex]\[
9^3 = 9 \times 9 \times 9 = 729
\][/tex]
3. Multiply the result by [tex]\(\frac{1}{9}\)[/tex].
Now, substitute [tex]\( 9^3 = 729 \)[/tex] back into the equation:
[tex]\[
f(3) = \left(\frac{1}{9}\right) \times 729
\][/tex]
4. Perform the multiplication.
Divide 729 by 9 since multiplying by [tex]\(\frac{1}{9}\)[/tex] is the same as dividing by 9:
[tex]\[
\frac{729}{9} = 81
\][/tex]
Therefore, [tex]\( f(3) = 81 \)[/tex].
The correct option is B. 81.
