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

Answer :

Sure! Let's solve the problem step by step.

The function we're given is:

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

We need to find [tex]\( f(3) \)[/tex].

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

So, [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 729.

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

4. Simplify [tex]\(\frac{729}{9}\)[/tex].

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

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

Therefore, the correct answer is:

B. 81