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Answer :
To find [tex]\( f(3) \)[/tex] for the given function [tex]\( f(x) = \left(\frac{1}{9}\right)\left(9^x\right) \)[/tex], we need to substitute [tex]\( x = 3 \)[/tex] into the function and simplify:
1. Start with the function:
[tex]\[
f(x) = \left(\frac{1}{9}\right)\left(9^x\right)
\][/tex]
2. Substitute [tex]\( x = 3 \)[/tex] into the equation:
[tex]\[
f(3) = \left(\frac{1}{9}\right)\left(9^3\right)
\][/tex]
3. Calculate [tex]\( 9^3 \)[/tex]. Nine cubed means multiplying 9 by itself three times:
[tex]\[
9 \times 9 \times 9 = 729
\][/tex]
4. Now, substitute [tex]\( 9^3 \)[/tex] with 729 in the equation:
[tex]\[
f(3) = \left(\frac{1}{9}\right) \times 729
\][/tex]
5. Multiply [tex]\( \frac{1}{9} \)[/tex] by 729:
[tex]\[
\frac{1}{9} \times 729 = 81
\][/tex]
Therefore, the value of [tex]\( f(3) \)[/tex] is [tex]\( 81 \)[/tex].
The correct answer is C. [tex]\( 81 \)[/tex].
1. Start with the function:
[tex]\[
f(x) = \left(\frac{1}{9}\right)\left(9^x\right)
\][/tex]
2. Substitute [tex]\( x = 3 \)[/tex] into the equation:
[tex]\[
f(3) = \left(\frac{1}{9}\right)\left(9^3\right)
\][/tex]
3. Calculate [tex]\( 9^3 \)[/tex]. Nine cubed means multiplying 9 by itself three times:
[tex]\[
9 \times 9 \times 9 = 729
\][/tex]
4. Now, substitute [tex]\( 9^3 \)[/tex] with 729 in the equation:
[tex]\[
f(3) = \left(\frac{1}{9}\right) \times 729
\][/tex]
5. Multiply [tex]\( \frac{1}{9} \)[/tex] by 729:
[tex]\[
\frac{1}{9} \times 729 = 81
\][/tex]
Therefore, the value of [tex]\( f(3) \)[/tex] is [tex]\( 81 \)[/tex].
The correct answer is C. [tex]\( 81 \)[/tex].
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