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Answer :
We are given the function
[tex]$$
f(x) = \frac{1}{9} \cdot 9^x.
$$[/tex]
To find [tex]$f(3)$[/tex], we substitute [tex]$x = 3$[/tex]:
[tex]$$
f(3) = \frac{1}{9} \cdot 9^3.
$$[/tex]
Now, calculate [tex]$9^3$[/tex]:
[tex]$$
9^3 = 9 \cdot 9 \cdot 9 = 729.
$$[/tex]
Then, substitute back into the expression for [tex]$f(3)$[/tex]:
[tex]$$
f(3) = \frac{1}{9} \cdot 729.
$$[/tex]
Divide [tex]$729$[/tex] by [tex]$9$[/tex]:
[tex]$$
\frac{729}{9} = 81.
$$[/tex]
Thus, the final answer is:
[tex]$$
f(3) = 81.
$$[/tex]
This corresponds to option D.
[tex]$$
f(x) = \frac{1}{9} \cdot 9^x.
$$[/tex]
To find [tex]$f(3)$[/tex], we substitute [tex]$x = 3$[/tex]:
[tex]$$
f(3) = \frac{1}{9} \cdot 9^3.
$$[/tex]
Now, calculate [tex]$9^3$[/tex]:
[tex]$$
9^3 = 9 \cdot 9 \cdot 9 = 729.
$$[/tex]
Then, substitute back into the expression for [tex]$f(3)$[/tex]:
[tex]$$
f(3) = \frac{1}{9} \cdot 729.
$$[/tex]
Divide [tex]$729$[/tex] by [tex]$9$[/tex]:
[tex]$$
\frac{729}{9} = 81.
$$[/tex]
Thus, the final answer is:
[tex]$$
f(3) = 81.
$$[/tex]
This corresponds to option D.
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