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

Answer :

Sure! Let's calculate [tex]\( f(3) \)[/tex] for the function [tex]\( f(x) = \left(\frac{1}{9}\right)\left(9^x\right) \)[/tex].

1. Substitute [tex]\( x = 3 \)[/tex] into the function:
We want to find [tex]\( f(3) \)[/tex]. So, replace [tex]\( x \)[/tex] with 3 in the equation:
[tex]\[
f(3) = \left(\frac{1}{9}\right)\left(9^3\right)
\][/tex]

2. Calculate [tex]\( 9^3 \)[/tex]:
This means multiplying 9 by itself three times:
[tex]\[
9^3 = 9 \times 9 \times 9 = 729
\][/tex]

3. Calculate [tex]\( \left(\frac{1}{9}\right) \times 729 \)[/tex]:
Now, multiply [tex]\(\frac{1}{9}\)[/tex] by 729:
[tex]\[
f(3) = \left(\frac{1}{9}\right) \times 729 = \frac{729}{9} = 81
\][/tex]

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

Therefore, the correct answer is C. 81.

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