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

Answer :

To solve the 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 are the steps:

1. Substitute 3 for [tex]\( x \)[/tex] in the function:
We have [tex]\( f(3) = \left(\frac{1}{9}\right) \left(9^3\right) \)[/tex].

2. Calculate [tex]\( 9^3 \)[/tex]:
[tex]\( 9^3 \)[/tex] 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 [tex]\( 729 \)[/tex] by [tex]\( \frac{1}{9} \)[/tex]:
[tex]\[
f(3) = \frac{1}{9} \times 729 = \frac{729}{9} = 81
\][/tex]

So, the value of [tex]\( f(3) \)[/tex] is 81.

Therefore, the correct answer is [tex]\( \boxed{81} \)[/tex].

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