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Answer :
To find the value of [tex]\( f(3) \)[/tex] for the function [tex]\( f(x) = \left(\frac{1}{9}\right)\left(9^x\right) \)[/tex], let's follow these steps:
1. Understand the function: The function given is [tex]\( f(x) = \left(\frac{1}{9}\right)\left(9^x\right) \)[/tex].
2. Substitute [tex]\( x = 3 \)[/tex]: We need to find [tex]\( f(3) \)[/tex], so we substitute 3 in place of [tex]\( x \)[/tex] in the function:
[tex]\[
f(3) = \left(\frac{1}{9}\right)\left(9^3\right)
\][/tex]
3. Calculate [tex]\( 9^3 \)[/tex]:
- [tex]\( 9^3 \)[/tex] means multiplying 9 by itself three times:
[tex]\[
9 \times 9 \times 9 = 729
\][/tex]
4. Multiply by [tex]\(\frac{1}{9}\)[/tex]:
- Take the result of [tex]\( 9^3 \)[/tex] which is 729 and multiply it by [tex]\(\frac{1}{9}\)[/tex]:
[tex]\[
\frac{1}{9} \times 729 = \frac{729}{9} = 81
\][/tex]
So, the value of [tex]\( f(3) \)[/tex] is 81.
Therefore, the correct answer is [tex]\( \boxed{81} \)[/tex].
1. Understand the function: The function given is [tex]\( f(x) = \left(\frac{1}{9}\right)\left(9^x\right) \)[/tex].
2. Substitute [tex]\( x = 3 \)[/tex]: We need to find [tex]\( f(3) \)[/tex], so we substitute 3 in place of [tex]\( x \)[/tex] in the function:
[tex]\[
f(3) = \left(\frac{1}{9}\right)\left(9^3\right)
\][/tex]
3. Calculate [tex]\( 9^3 \)[/tex]:
- [tex]\( 9^3 \)[/tex] means multiplying 9 by itself three times:
[tex]\[
9 \times 9 \times 9 = 729
\][/tex]
4. Multiply by [tex]\(\frac{1}{9}\)[/tex]:
- Take the result of [tex]\( 9^3 \)[/tex] which is 729 and multiply it by [tex]\(\frac{1}{9}\)[/tex]:
[tex]\[
\frac{1}{9} \times 729 = \frac{729}{9} = 81
\][/tex]
So, the value of [tex]\( f(3) \)[/tex] is 81.
Therefore, the correct answer is [tex]\( \boxed{81} \)[/tex].
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