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

Answer :

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

Step-by-step Solution:

1. Substitute [tex]\( x = 3 \)[/tex] into the function:

The function is defined as [tex]\( f(x) = \left(\frac{1}{9}\right)\left(9^x\right) \)[/tex].

So, substitute [tex]\( x = 3 \)[/tex] into the function to get:
[tex]\[
f(3) = \left(\frac{1}{9}\right)\left(9^3\right)
\][/tex]

2. Calculate [tex]\( 9^3 \)[/tex]:

We need to calculate [tex]\( 9^3 \)[/tex], which means multiplying 9 by itself three times:
[tex]\[
9^3 = 9 \times 9 \times 9 = 729
\][/tex]

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

Now, multiply the result by [tex]\(\frac{1}{9}\)[/tex] as per the function:
[tex]\[
f(3) = \left(\frac{1}{9}\right) \times 729
\][/tex]

Simplifying this calculation gives:
[tex]\[
f(3) = \frac{729}{9} = 81
\][/tex]

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

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