Answer :
To solve the problem, we need to calculate the value of [tex]\( f(3) \)[/tex] for the function [tex]\( f(x) = \left(\frac{1}{9}\right)\left(9^x\right) \)[/tex].
Here's how we can do this step-by-step:
1. Identify the function:
The function given is [tex]\( f(x) = \left(\frac{1}{9}\right) \cdot 9^x \)[/tex].
2. Substitute [tex]\( x \)[/tex] with 3:
We want to find [tex]\( f(3) \)[/tex], so we substitute [tex]\( x = 3 \)[/tex] into the function:
[tex]\( f(3) = \left(\frac{1}{9}\right) \cdot 9^3 \)[/tex].
3. Calculate [tex]\( 9^3 \)[/tex]:
First, calculate [tex]\( 9^3 \)[/tex], which means 9 multiplied by itself three times:
[tex]\( 9^3 = 9 \times 9 \times 9 = 729 \)[/tex].
4. Multiply by [tex]\( \frac{1}{9} \)[/tex]:
Now, multiply [tex]\( 729 \)[/tex] by [tex]\( \frac{1}{9} \)[/tex]:
[tex]\( \left(\frac{1}{9}\right) \times 729 = \frac{729}{9} = 81 \)[/tex].
So, the value of [tex]\( f(3) \)[/tex] is 81.
Thus, the correct answer is B. 81.
Here's how we can do this step-by-step:
1. Identify the function:
The function given is [tex]\( f(x) = \left(\frac{1}{9}\right) \cdot 9^x \)[/tex].
2. Substitute [tex]\( x \)[/tex] with 3:
We want to find [tex]\( f(3) \)[/tex], so we substitute [tex]\( x = 3 \)[/tex] into the function:
[tex]\( f(3) = \left(\frac{1}{9}\right) \cdot 9^3 \)[/tex].
3. Calculate [tex]\( 9^3 \)[/tex]:
First, calculate [tex]\( 9^3 \)[/tex], which means 9 multiplied by itself three times:
[tex]\( 9^3 = 9 \times 9 \times 9 = 729 \)[/tex].
4. Multiply by [tex]\( \frac{1}{9} \)[/tex]:
Now, multiply [tex]\( 729 \)[/tex] by [tex]\( \frac{1}{9} \)[/tex]:
[tex]\( \left(\frac{1}{9}\right) \times 729 = \frac{729}{9} = 81 \)[/tex].
So, the value of [tex]\( f(3) \)[/tex] is 81.
Thus, the correct answer is B. 81.
