Answer :
Sure! Let's solve the problem step by step.
The function we're given is:
[tex]\[ f(x) = \left(\frac{1}{9}\right)\left(9^x\right) \][/tex]
We need to find [tex]\( f(3) \)[/tex].
1. Substitute [tex]\( x = 3 \)[/tex] into the function.
So, [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 [tex]\(\frac{1}{9}\)[/tex] by 729.
[tex]\[ f(3) = \left(\frac{1}{9}\right) \times 729 = \frac{729}{9} \][/tex]
4. Simplify [tex]\(\frac{729}{9}\)[/tex].
[tex]\[ \frac{729}{9} = 81 \][/tex]
So, the value of [tex]\( f(3) \)[/tex] is 81.
Therefore, the correct answer is:
B. 81
The function we're given is:
[tex]\[ f(x) = \left(\frac{1}{9}\right)\left(9^x\right) \][/tex]
We need to find [tex]\( f(3) \)[/tex].
1. Substitute [tex]\( x = 3 \)[/tex] into the function.
So, [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 [tex]\(\frac{1}{9}\)[/tex] by 729.
[tex]\[ f(3) = \left(\frac{1}{9}\right) \times 729 = \frac{729}{9} \][/tex]
4. Simplify [tex]\(\frac{729}{9}\)[/tex].
[tex]\[ \frac{729}{9} = 81 \][/tex]
So, the value of [tex]\( f(3) \)[/tex] is 81.
Therefore, the correct answer is:
B. 81
