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. Understand the Function: The given function is [tex]\( f(x) = \left(\frac{1}{9}\right)\left(9^x\right) \)[/tex]. It involves a power function [tex]\( 9^x \)[/tex] which is then multiplied by [tex]\(\frac{1}{9}\)[/tex].
2. Substitute the Value: We need to find [tex]\( f(3) \)[/tex]. So, substitute [tex]\( x = 3 \)[/tex] into the function:
[tex]\[
f(3) = \left(\frac{1}{9}\right)\left(9^3\right)
\][/tex]
3. Calculate [tex]\( 9^3 \)[/tex]: First, calculate [tex]\( 9^3 \)[/tex].
[tex]\[
9^3 = 9 \times 9 \times 9 = 729
\][/tex]
4. Multiply by [tex]\(\frac{1}{9}\)[/tex]: Next, multiply 729 by [tex]\(\frac{1}{9}\)[/tex]:
[tex]\[
f(3) = \left(\frac{1}{9}\right)\times 729 = \frac{729}{9}
\][/tex]
5. Simplify the Expression: Divide 729 by 9:
[tex]\[
\frac{729}{9} = 81
\][/tex]
Therefore, the value of [tex]\( f(3) \)[/tex] is [tex]\( 81 \)[/tex], which corresponds to option D.
1. Understand the Function: The given function is [tex]\( f(x) = \left(\frac{1}{9}\right)\left(9^x\right) \)[/tex]. It involves a power function [tex]\( 9^x \)[/tex] which is then multiplied by [tex]\(\frac{1}{9}\)[/tex].
2. Substitute the Value: We need to find [tex]\( f(3) \)[/tex]. So, substitute [tex]\( x = 3 \)[/tex] into the function:
[tex]\[
f(3) = \left(\frac{1}{9}\right)\left(9^3\right)
\][/tex]
3. Calculate [tex]\( 9^3 \)[/tex]: First, calculate [tex]\( 9^3 \)[/tex].
[tex]\[
9^3 = 9 \times 9 \times 9 = 729
\][/tex]
4. Multiply by [tex]\(\frac{1}{9}\)[/tex]: Next, multiply 729 by [tex]\(\frac{1}{9}\)[/tex]:
[tex]\[
f(3) = \left(\frac{1}{9}\right)\times 729 = \frac{729}{9}
\][/tex]
5. Simplify the Expression: Divide 729 by 9:
[tex]\[
\frac{729}{9} = 81
\][/tex]
Therefore, the value of [tex]\( f(3) \)[/tex] is [tex]\( 81 \)[/tex], which corresponds to option D.
