High School

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

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

Answer :

We need to find the value of [tex]\( f(3) \)[/tex] for the function [tex]\( f(x) = \left(\frac{1}{9}\right)\left(9^x\right) \)[/tex].

Let's evaluate [tex]\( f(3) \)[/tex] step-by-step:

1. Identify the expression for [tex]\( f(x) \)[/tex]:
[tex]\[
f(x) = \left(\frac{1}{9}\right) \times (9^x)
\][/tex]

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

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

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

5. Evaluate the expression:
[tex]\[
\left(\frac{1}{9}\right) \times 729 = \frac{729}{9} = 81
\][/tex]

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

The correct answer is B. 81.