Answer :
Let's solve the problem step by step:
Given the function:
[tex]\[ f(x) = \left(\frac{1}{9}\right)\left(9^x\right) \][/tex]
We need to find [tex]\( f(3) \)[/tex]. To do this, substitute [tex]\( x = 3 \)[/tex] into the function:
1. Substitute 3 for [tex]\( x \)[/tex]:
[tex]\[ f(3) = \left(\frac{1}{9}\right)\left(9^3\right) \][/tex]
2. Calculate [tex]\( 9^3 \)[/tex]:
[tex]\[ 9^3 = 9 \times 9 \times 9 = 729 \][/tex]
3. Multiply by [tex]\(\frac{1}{9}\)[/tex]:
[tex]\[ f(3) = \frac{1}{9} \times 729 \][/tex]
4. Simplify the expression:
To multiply 729 by [tex]\(\frac{1}{9}\)[/tex], divide 729 by 9:
[tex]\[ \frac{729}{9} = 81 \][/tex]
So, [tex]\( f(3) = 81 \)[/tex].
Therefore, the answer is A. 81.
Given the function:
[tex]\[ f(x) = \left(\frac{1}{9}\right)\left(9^x\right) \][/tex]
We need to find [tex]\( f(3) \)[/tex]. To do this, substitute [tex]\( x = 3 \)[/tex] into the function:
1. Substitute 3 for [tex]\( x \)[/tex]:
[tex]\[ f(3) = \left(\frac{1}{9}\right)\left(9^3\right) \][/tex]
2. Calculate [tex]\( 9^3 \)[/tex]:
[tex]\[ 9^3 = 9 \times 9 \times 9 = 729 \][/tex]
3. Multiply by [tex]\(\frac{1}{9}\)[/tex]:
[tex]\[ f(3) = \frac{1}{9} \times 729 \][/tex]
4. Simplify the expression:
To multiply 729 by [tex]\(\frac{1}{9}\)[/tex], divide 729 by 9:
[tex]\[ \frac{729}{9} = 81 \][/tex]
So, [tex]\( f(3) = 81 \)[/tex].
Therefore, the answer is A. 81.
