High School

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

Answer :

Let's solve the problem step-by-step:

We are given the function [tex]\( f(x) = \left(\frac{1}{9}\right) \left(9^x\right) \)[/tex].

To find [tex]\( f(3) \)[/tex], we will substitute [tex]\( x = 3 \)[/tex] into the function:

1. Substitute [tex]\( x = 3 \)[/tex] into the function:
[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. Now compute [tex]\( \left(\frac{1}{9}\right) \times 729 \)[/tex]:
[tex]\[
\left(\frac{1}{9}\right) \times 729 = \frac{729}{9} = 81
\][/tex]

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

The correct answer is [tex]\( \boxed{81} \)[/tex].