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

Answer :

To find [tex]\( f(3) \)[/tex] for the function [tex]\( f(x) = \left(\frac{1}{9}\right)\left(9^x\right) \)[/tex], we will substitute [tex]\( x = 3 \)[/tex] into the function and calculate the result.

Here's a step-by-step process:

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]\[
9^3 = 9 \times 9 \times 9 = 729
\][/tex]

3. Multiply [tex]\(\frac{1}{9}\)[/tex] by [tex]\( 729 \)[/tex]:

[tex]\[
f(3) = \left(\frac{1}{9}\right) \times 729 = \frac{729}{9}
\][/tex]

4. Divide 729 by 9 to get the final answer:

[tex]\[
\frac{729}{9} = 81
\][/tex]

Therefore, the value of [tex]\( f(3) \)[/tex] is [tex]\( 81 \)[/tex], which corresponds to option D.

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