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

Answer :

Sure! Let's solve the problem step-by-step.

We're given the function [tex]\( f(x) = \left(\frac{1}{9}\right)\left(9^x\right) \)[/tex] and we need to find [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. Calculate [tex]\( f(3) \)[/tex]:
[tex]\[
f(3) = \left(\frac{1}{9}\right) \times 729
\][/tex]

4. Divide 729 by 9:
[tex]\[
\frac{729}{9} = 81
\][/tex]

Therefore, [tex]\( f(3) = 81 \)[/tex].

The correct answer is B. 81.

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