Answer :
Sure! Let's find [tex]\( f(3) \)[/tex] for the function [tex]\( f(x) = \left(\frac{1}{9}\right)\left(9^x\right) \)[/tex].
1. Substitute [tex]\( x = 3 \)[/tex]:
We need to evaluate the function at [tex]\( x = 3 \)[/tex]:
[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].
We start by calculating [tex]\( 9 \times 9 = 81 \)[/tex].
Then, multiply 81 by 9:
[tex]\( 81 \times 9 = 729 \)[/tex].
3. Divide by 9:
Now, substitute back into the function:
[tex]\[
f(3) = \left(\frac{1}{9}\right) \times 729
\][/tex]
Dividing 729 by 9 gives:
[tex]\[
\frac{729}{9} = 81
\][/tex]
So, the value of [tex]\( f(3) \)[/tex] is [tex]\( 81 \)[/tex].
Therefore, the correct answer is C. 81.
1. Substitute [tex]\( x = 3 \)[/tex]:
We need to evaluate the function at [tex]\( x = 3 \)[/tex]:
[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].
We start by calculating [tex]\( 9 \times 9 = 81 \)[/tex].
Then, multiply 81 by 9:
[tex]\( 81 \times 9 = 729 \)[/tex].
3. Divide by 9:
Now, substitute back into the function:
[tex]\[
f(3) = \left(\frac{1}{9}\right) \times 729
\][/tex]
Dividing 729 by 9 gives:
[tex]\[
\frac{729}{9} = 81
\][/tex]
So, the value of [tex]\( f(3) \)[/tex] is [tex]\( 81 \)[/tex].
Therefore, the correct answer is C. 81.
