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

Answer :

To find the value of the function [tex]\( f(x) = \left(\frac{1}{9}\right)\left(9^x\right) \)[/tex] at [tex]\( x = 3 \)[/tex], follow these steps:

1. Substitute [tex]\( x = 3 \)[/tex] into the function [tex]\( f(x) \)[/tex]. So, the expression becomes:
[tex]\[
f(3) = \left(\frac{1}{9}\right) \left(9^3\right)
\][/tex]

2. Calculate [tex]\( 9^3 \)[/tex]:
[tex]\[
9^3 = 9 \times 9 \times 9 = 81 \times 9 = 729
\][/tex]

3. Substitute [tex]\( 729 \)[/tex] back into the expression:
[tex]\[
f(3) = \left(\frac{1}{9}\right) \times 729
\][/tex]

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

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

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

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