Answer :
To find [tex]\( f(3) \)[/tex] for the function [tex]\( f(x) = \left(\frac{1}{9}\right)\left(9^x\right) \)[/tex], let's follow these steps:
1. Identify the function:
We have [tex]\( f(x) = \left(\frac{1}{9}\right) \times 9^x \)[/tex].
2. Substitute [tex]\( x = 3 \)[/tex] into the function:
Replace [tex]\( x \)[/tex] in the function with 3:
[tex]\[
f(3) = \left(\frac{1}{9}\right) \times 9^3
\][/tex]
3. Calculate [tex]\( 9^3 \)[/tex]:
[tex]\( 9^3 \)[/tex] means multiplying 9 by itself three times:
[tex]\[
9 \times 9 \times 9 = 81 \times 9 = 729
\][/tex]
4. Multiply by [tex]\(\frac{1}{9}\)[/tex]:
Now, multiply the result of [tex]\( 9^3 \)[/tex] by [tex]\(\frac{1}{9}\)[/tex]:
[tex]\[
f(3) = \left(\frac{1}{9}\right) \times 729 = \frac{729}{9}
\][/tex]
5. Simplify the fraction:
Divide 729 by 9:
[tex]\[
\frac{729}{9} = 81
\][/tex]
Thus, the value of [tex]\( f(3) \)[/tex] is 81. Therefore, the correct answer is:
B. 81
1. Identify the function:
We have [tex]\( f(x) = \left(\frac{1}{9}\right) \times 9^x \)[/tex].
2. Substitute [tex]\( x = 3 \)[/tex] into the function:
Replace [tex]\( x \)[/tex] in the function with 3:
[tex]\[
f(3) = \left(\frac{1}{9}\right) \times 9^3
\][/tex]
3. Calculate [tex]\( 9^3 \)[/tex]:
[tex]\( 9^3 \)[/tex] means multiplying 9 by itself three times:
[tex]\[
9 \times 9 \times 9 = 81 \times 9 = 729
\][/tex]
4. Multiply by [tex]\(\frac{1}{9}\)[/tex]:
Now, multiply the result of [tex]\( 9^3 \)[/tex] by [tex]\(\frac{1}{9}\)[/tex]:
[tex]\[
f(3) = \left(\frac{1}{9}\right) \times 729 = \frac{729}{9}
\][/tex]
5. Simplify the fraction:
Divide 729 by 9:
[tex]\[
\frac{729}{9} = 81
\][/tex]
Thus, the value of [tex]\( f(3) \)[/tex] is 81. Therefore, the correct answer is:
B. 81
