Answer :
To find the value of [tex]\( f(3) \)[/tex] for the given 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:
We substitute [tex]\( 3 \)[/tex] for [tex]\( x \)[/tex] in 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 [tex]\( 9 \times 9 \times 9 \)[/tex]. Calculate this step-by-step:
- First, [tex]\( 9 \times 9 = 81 \)[/tex].
- Then, [tex]\( 81 \times 9 = 729 \)[/tex].
So, [tex]\( 9^3 = 729 \)[/tex].
3. Multiply by [tex]\(\frac{1}{9}\)[/tex]:
Now, calculate [tex]\(\frac{1}{9} \times 729\)[/tex].
- When you divide 729 by 9, you get 81 because [tex]\( 729 \div 9 = 81 \)[/tex].
Thus, [tex]\( f(3) = 81 \)[/tex].
The correct answer is A. 81.
1. Substitute [tex]\( x = 3 \)[/tex] into the function:
We substitute [tex]\( 3 \)[/tex] for [tex]\( x \)[/tex] in 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 [tex]\( 9 \times 9 \times 9 \)[/tex]. Calculate this step-by-step:
- First, [tex]\( 9 \times 9 = 81 \)[/tex].
- Then, [tex]\( 81 \times 9 = 729 \)[/tex].
So, [tex]\( 9^3 = 729 \)[/tex].
3. Multiply by [tex]\(\frac{1}{9}\)[/tex]:
Now, calculate [tex]\(\frac{1}{9} \times 729\)[/tex].
- When you divide 729 by 9, you get 81 because [tex]\( 729 \div 9 = 81 \)[/tex].
Thus, [tex]\( f(3) = 81 \)[/tex].
The correct answer is A. 81.
