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Answer :
To find [tex]\( f(3) \)[/tex] given the function [tex]\( f(x) = \left(\frac{1}{9}\right)\left(9^x\right) \)[/tex], we follow these steps:
1. Substitute the value into the function: To find [tex]\( f(3) \)[/tex], replace [tex]\( x \)[/tex] with 3 in the function:
[tex]\[
f(3) = \left(\frac{1}{9}\right)\left(9^3\right)
\][/tex]
2. Calculate [tex]\( 9^3 \)[/tex]: First, we need to calculate [tex]\( 9^3 \)[/tex].
- [tex]\( 9^3 \)[/tex] means [tex]\( 9 \times 9 \times 9 \)[/tex].
- First, calculate [tex]\( 9 \times 9 = 81 \)[/tex].
- Then, multiply 81 by 9 to get 729.
[tex]\[
9^3 = 729
\][/tex]
3. Multiply by [tex]\(\frac{1}{9}\)[/tex]: Now, take the result from the previous step and multiply it by [tex]\(\frac{1}{9}\)[/tex]:
[tex]\[
\left(\frac{1}{9}\right) \times 729 = \frac{729}{9} = 81
\][/tex]
Therefore, the value of [tex]\( f(3) \)[/tex] is [tex]\( 81 \)[/tex].
The correct answer is:
A. 81
1. Substitute the value into the function: To find [tex]\( f(3) \)[/tex], replace [tex]\( x \)[/tex] with 3 in the function:
[tex]\[
f(3) = \left(\frac{1}{9}\right)\left(9^3\right)
\][/tex]
2. Calculate [tex]\( 9^3 \)[/tex]: First, we need to calculate [tex]\( 9^3 \)[/tex].
- [tex]\( 9^3 \)[/tex] means [tex]\( 9 \times 9 \times 9 \)[/tex].
- First, calculate [tex]\( 9 \times 9 = 81 \)[/tex].
- Then, multiply 81 by 9 to get 729.
[tex]\[
9^3 = 729
\][/tex]
3. Multiply by [tex]\(\frac{1}{9}\)[/tex]: Now, take the result from the previous step and multiply it by [tex]\(\frac{1}{9}\)[/tex]:
[tex]\[
\left(\frac{1}{9}\right) \times 729 = \frac{729}{9} = 81
\][/tex]
Therefore, the value of [tex]\( f(3) \)[/tex] is [tex]\( 81 \)[/tex].
The correct answer is:
A. 81
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