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

Answer :

Sure! Let's find [tex]\( f(3) \)[/tex] for the function [tex]\( f(x) = \left(\frac{1}{9}\right)\left(9^x\right) \)[/tex].

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

We need to evaluate the function at [tex]\( x = 3 \)[/tex]:

[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].

We start by calculating [tex]\( 9 \times 9 = 81 \)[/tex].

Then, multiply 81 by 9:

[tex]\( 81 \times 9 = 729 \)[/tex].

3. Divide by 9:

Now, substitute back into the function:

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

Dividing 729 by 9 gives:

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

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

Therefore, the correct answer is C. 81.

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