College

If [tex]f(x)=\left(\frac{1}{9}\right)\left(9^x\right)[/tex], what is [tex]f(3)[/tex]?

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

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.