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

Answer :

Let's solve the problem step by step:

Given the function:
[tex]\[ f(x) = \left(\frac{1}{9}\right)\left(9^x\right) \][/tex]

We need to find [tex]\( f(3) \)[/tex]. To do this, substitute [tex]\( x = 3 \)[/tex] into the function:

1. Substitute 3 for [tex]\( x \)[/tex]:
[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. Multiply by [tex]\(\frac{1}{9}\)[/tex]:
[tex]\[ f(3) = \frac{1}{9} \times 729 \][/tex]

4. Simplify the expression:
To multiply 729 by [tex]\(\frac{1}{9}\)[/tex], divide 729 by 9:
[tex]\[ \frac{729}{9} = 81 \][/tex]

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

Therefore, the answer is A. 81.

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