High School

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

Answer :

We are given the function

[tex]$$
f(x)=\frac{1}{9}\cdot 9^x.
$$[/tex]

To evaluate [tex]$f(3)$[/tex], follow these steps:

1. Substitute [tex]$x=3$[/tex] into the function:

[tex]$$
f(3)=\frac{1}{9}\cdot 9^3.
$$[/tex]

2. Calculate [tex]$9^3$[/tex]:

[tex]$$
9^3=9\cdot9\cdot9=729.
$$[/tex]

3. Now, multiply by the coefficient:

[tex]$$
f(3)=\frac{1}{9}\cdot729=\frac{729}{9}=81.
$$[/tex]

Thus, the value of [tex]$f(3)$[/tex] is [tex]$\boxed{81}$[/tex].