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If [tex]$f(x)=\left(\frac{1}{9}\right)\left(9^x\right)$[/tex], what is [tex]$f(3)$[/tex]?

A. 729
B. [tex]$\frac{1}{729}$[/tex]
C. 81
D. [tex]$\frac{1}{81}$[/tex]

Answer :

To find [tex]\( f(3) \)[/tex] for the function [tex]\( f(x) = \left(\frac{1}{9}\right)\left(9^x\right) \)[/tex], we can follow these steps:

1. Substitute the Value of [tex]\( x \)[/tex]: Replace [tex]\( x \)[/tex] with 3 in the function.
[tex]\[
f(3) = \left(\frac{1}{9}\right)\left(9^3\right)
\][/tex]

2. Calculate [tex]\( 9^3 \)[/tex]: Find the value of [tex]\( 9^3 \)[/tex].
[tex]\[
9^3 = 9 \times 9 \times 9 = 729
\][/tex]

3. Multiply by [tex]\(\frac{1}{9}\)[/tex]: Once we have [tex]\( 9^3 = 729 \)[/tex], we multiply it by [tex]\(\frac{1}{9}\)[/tex].
[tex]\[
f(3) = \left(\frac{1}{9}\right) \times 729
\][/tex]

4. Simplify the Expression: Calculate the final multiplication.
[tex]\[
f(3) = \frac{729}{9} = 81
\][/tex]

Thus, the value of [tex]\( f(3) \)[/tex] is 81. Therefore, the correct answer is:

C. 81

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