Answer :
To solve the problem and find [tex]\( f(3) \)[/tex] for the function [tex]\( f(x) = \left( \frac{1}{9} \right) \left( 9^x \right) \)[/tex], follow these steps:
1. Substitute [tex]\( x = 3 \)[/tex] into the function:
[tex]\[
f(3) = \left( \frac{1}{9} \right) \left( 9^3 \right)
\][/tex]
2. Calculate [tex]\( 9^3 \)[/tex]:
- [tex]\( 9^3 \)[/tex] means multiplying 9 by itself three times.
- [tex]\( 9 \times 9 = 81 \)[/tex]
- Then, multiply 81 by 9:
[tex]\( 81 \times 9 = 729 \)[/tex]
3. Substitute the value of [tex]\( 9^3 \)[/tex] into the function:
[tex]\[
f(3) = \left( \frac{1}{9} \right) \times 729
\][/tex]
4. Multiply [tex]\( \frac{1}{9} \)[/tex] by 729:
- Dividing 729 by 9 gives 81.
Therefore, the value of [tex]\( f(3) \)[/tex] is 81.
So, the correct answer is B. 81.
1. Substitute [tex]\( x = 3 \)[/tex] into the function:
[tex]\[
f(3) = \left( \frac{1}{9} \right) \left( 9^3 \right)
\][/tex]
2. Calculate [tex]\( 9^3 \)[/tex]:
- [tex]\( 9^3 \)[/tex] means multiplying 9 by itself three times.
- [tex]\( 9 \times 9 = 81 \)[/tex]
- Then, multiply 81 by 9:
[tex]\( 81 \times 9 = 729 \)[/tex]
3. Substitute the value of [tex]\( 9^3 \)[/tex] into the function:
[tex]\[
f(3) = \left( \frac{1}{9} \right) \times 729
\][/tex]
4. Multiply [tex]\( \frac{1}{9} \)[/tex] by 729:
- Dividing 729 by 9 gives 81.
Therefore, the value of [tex]\( f(3) \)[/tex] is 81.
So, the correct answer is B. 81.
