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

Answer :

Sure! Let's solve this step-by-step:

We are given the function [tex]\( f(x) = \left(\frac{1}{9}\right)\left(9^x\right) \)[/tex] and need to find [tex]\( f(3) \)[/tex].

1. Substitute [tex]\( x = 3 \)[/tex] into the function.
This gives us:
[tex]\[
f(3) = \left(\frac{1}{9}\right) \left(9^3\right)
\][/tex]

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

3. Multiply [tex]\(\frac{1}{9}\)[/tex] by [tex]\( 729 \)[/tex].
So, we have:
[tex]\[
f(3) = \frac{1}{9} \times 729
\][/tex]
When you multiply [tex]\(\frac{1}{9}\)[/tex] by 729, you divide 729 by 9:
[tex]\[
729 \div 9 = 81
\][/tex]

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

The correct choice is A. 81.

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