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

Answer :

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

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

[tex]\[
f(3) = \left(\frac{1}{9}\right)\left(9^3\right)
\][/tex]

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

[tex]\( 9^3 \)[/tex] means [tex]\( 9 \times 9 \times 9 \)[/tex]. Calculate this step-by-step:

- First, [tex]\( 9 \times 9 = 81 \)[/tex].
- Then, [tex]\( 81 \times 9 = 729 \)[/tex].

So, [tex]\( 9^3 = 729 \)[/tex].

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

Now, calculate [tex]\(\frac{1}{9} \times 729\)[/tex].

- When you divide 729 by 9, you get 81 because [tex]\( 729 \div 9 = 81 \)[/tex].

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

The correct answer is A. 81.

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