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Answer :
We need 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 evaluate [tex]\( f(3) \)[/tex] step-by-step:
1. Identify the expression for [tex]\( f(x) \)[/tex]:
[tex]\[
f(x) = \left(\frac{1}{9}\right) \times (9^x)
\][/tex]
2. Substitute [tex]\( x = 3 \)[/tex] into the function:
[tex]\[
f(3) = \left(\frac{1}{9}\right) \times (9^3)
\][/tex]
3. Calculate [tex]\( 9^3 \)[/tex]:
[tex]\[
9^3 = 9 \times 9 \times 9 = 729
\][/tex]
4. Substitute [tex]\( 9^3 \)[/tex] back into the function:
[tex]\[
f(3) = \left(\frac{1}{9}\right) \times 729
\][/tex]
5. Evaluate the expression:
[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 B. 81.
Let's evaluate [tex]\( f(3) \)[/tex] step-by-step:
1. Identify the expression for [tex]\( f(x) \)[/tex]:
[tex]\[
f(x) = \left(\frac{1}{9}\right) \times (9^x)
\][/tex]
2. Substitute [tex]\( x = 3 \)[/tex] into the function:
[tex]\[
f(3) = \left(\frac{1}{9}\right) \times (9^3)
\][/tex]
3. Calculate [tex]\( 9^3 \)[/tex]:
[tex]\[
9^3 = 9 \times 9 \times 9 = 729
\][/tex]
4. Substitute [tex]\( 9^3 \)[/tex] back into the function:
[tex]\[
f(3) = \left(\frac{1}{9}\right) \times 729
\][/tex]
5. Evaluate the expression:
[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 B. 81.
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