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Answer :
To solve for [tex]\( f(3) \)[/tex] when [tex]\( f(x) = \left(\frac{1}{9}\right)\left(9^x\right) \)[/tex], we can follow these steps:
1. Understand the Function:
- The function [tex]\( f(x) \)[/tex] is defined as [tex]\( f(x) = \frac{1}{9} \cdot 9^x \)[/tex].
2. Substitute [tex]\( x = 3 \)[/tex] into the Function:
- We want to find [tex]\( f(3) \)[/tex], so substitute 3 in place of [tex]\( x \)[/tex]:
[tex]\[ f(3) = \frac{1}{9} \cdot 9^3 \][/tex]
3. Calculate [tex]\( 9^3 \)[/tex]:
- Calculate [tex]\( 9^3 \)[/tex]:
[tex]\[ 9^3 = 9 \times 9 \times 9 = 729 \][/tex]
4. Multiply [tex]\( \frac{1}{9} \)[/tex] by [tex]\( 729 \)[/tex]:
- Multiply the result by [tex]\( \frac{1}{9} \)[/tex]:
[tex]\[ f(3) = \frac{1}{9} \cdot 729 = \frac{729}{9} \][/tex]
5. Simplify the Expression:
- Now, divide 729 by 9:
[tex]\[ \frac{729}{9} = 81 \][/tex]
So, the value of [tex]\( f(3) \)[/tex] is [tex]\( 81 \)[/tex].
Therefore, the correct answer is:
A. 81
1. Understand the Function:
- The function [tex]\( f(x) \)[/tex] is defined as [tex]\( f(x) = \frac{1}{9} \cdot 9^x \)[/tex].
2. Substitute [tex]\( x = 3 \)[/tex] into the Function:
- We want to find [tex]\( f(3) \)[/tex], so substitute 3 in place of [tex]\( x \)[/tex]:
[tex]\[ f(3) = \frac{1}{9} \cdot 9^3 \][/tex]
3. Calculate [tex]\( 9^3 \)[/tex]:
- Calculate [tex]\( 9^3 \)[/tex]:
[tex]\[ 9^3 = 9 \times 9 \times 9 = 729 \][/tex]
4. Multiply [tex]\( \frac{1}{9} \)[/tex] by [tex]\( 729 \)[/tex]:
- Multiply the result by [tex]\( \frac{1}{9} \)[/tex]:
[tex]\[ f(3) = \frac{1}{9} \cdot 729 = \frac{729}{9} \][/tex]
5. Simplify the Expression:
- Now, divide 729 by 9:
[tex]\[ \frac{729}{9} = 81 \][/tex]
So, the value of [tex]\( f(3) \)[/tex] is [tex]\( 81 \)[/tex].
Therefore, the correct answer is:
A. 81
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