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

Answer :

To find [tex]\( f(3) \)[/tex] for the function [tex]\( f(x) = \left(\frac{1}{9}\right)\left(9^x\right) \)[/tex], we need to follow these steps:

1. Substitute the given value of [tex]\( x \)[/tex] into the function.

We are looking for [tex]\( f(3) \)[/tex], so we 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].

To do this, multiply 9 by itself three times:
[tex]\[
9^3 = 9 \times 9 \times 9 = 729
\][/tex]

3. Multiply the result by [tex]\(\frac{1}{9}\)[/tex].

Now, substitute [tex]\( 9^3 = 729 \)[/tex] back into the equation:
[tex]\[
f(3) = \left(\frac{1}{9}\right) \times 729
\][/tex]

4. Perform the multiplication.

Divide 729 by 9 since multiplying by [tex]\(\frac{1}{9}\)[/tex] is the same as dividing by 9:
[tex]\[
\frac{729}{9} = 81
\][/tex]

Therefore, [tex]\( f(3) = 81 \)[/tex].

The correct option is B. 81.