Answer :
Sure, let's solve the problem step-by-step.
We are given the function [tex]\( f(x) = \left(\frac{1}{9}\right)\left(9^x\right) \)[/tex]. We need to find the value of [tex]\( f(3) \)[/tex].
1. 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]:
[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. Perform the multiplication:
[tex]\[
\frac{729}{9} = 81
\][/tex]
Thus, the value of [tex]\( f(3) \)[/tex] is [tex]\( 81 \)[/tex].
So, the correct answer is C. 81.
We are given the function [tex]\( f(x) = \left(\frac{1}{9}\right)\left(9^x\right) \)[/tex]. We need to find the value of [tex]\( f(3) \)[/tex].
1. 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]:
[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. Perform the multiplication:
[tex]\[
\frac{729}{9} = 81
\][/tex]
Thus, the value of [tex]\( f(3) \)[/tex] is [tex]\( 81 \)[/tex].
So, the correct answer is C. 81.
