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

Answer :

To solve the problem and find [tex]\( f(3) \)[/tex] for the 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:
[tex]\[
f(3) = \left( \frac{1}{9} \right) \left( 9^3 \right)
\][/tex]

2. Calculate [tex]\( 9^3 \)[/tex]:
- [tex]\( 9^3 \)[/tex] means multiplying 9 by itself three times.
- [tex]\( 9 \times 9 = 81 \)[/tex]
- Then, multiply 81 by 9:
[tex]\( 81 \times 9 = 729 \)[/tex]

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

4. Multiply [tex]\( \frac{1}{9} \)[/tex] by 729:
- Dividing 729 by 9 gives 81.

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

So, the correct answer is B. 81.

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