Answer :
Let's solve the problem step-by-step to find the value of [tex]\( f(3) \)[/tex].
Given the function:
[tex]\[ f(x) = \left( \frac{1}{9} \right) \left( 9^x \right) \][/tex]
We need to find [tex]\( f(3) \)[/tex].
Step 1: Substitute [tex]\( x = 3 \)[/tex] into the function:
[tex]\[ f(3) = \left( \frac{1}{9} \right) \left( 9^3 \right) \][/tex]
Step 2: Calculate [tex]\( 9^3 \)[/tex]:
[tex]\[ 9^3 = 9 \times 9 \times 9 = 81 \times 9 = 729 \][/tex]
Step 3: Now, multiply by [tex]\( \frac{1}{9} \)[/tex]:
[tex]\[ f(3) = \left( \frac{1}{9} \right) \left( 729 \right) \][/tex]
Step 4: Simplify the multiplication:
[tex]\[ \frac{1}{9} \times 729 = \frac{729}{9} = 81 \][/tex]
So, [tex]\( f(3) = 81 \)[/tex].
Therefore, the correct answer is:
[tex]\[ \boxed{81} \][/tex]
Given the function:
[tex]\[ f(x) = \left( \frac{1}{9} \right) \left( 9^x \right) \][/tex]
We need to find [tex]\( f(3) \)[/tex].
Step 1: Substitute [tex]\( x = 3 \)[/tex] into the function:
[tex]\[ f(3) = \left( \frac{1}{9} \right) \left( 9^3 \right) \][/tex]
Step 2: Calculate [tex]\( 9^3 \)[/tex]:
[tex]\[ 9^3 = 9 \times 9 \times 9 = 81 \times 9 = 729 \][/tex]
Step 3: Now, multiply by [tex]\( \frac{1}{9} \)[/tex]:
[tex]\[ f(3) = \left( \frac{1}{9} \right) \left( 729 \right) \][/tex]
Step 4: Simplify the multiplication:
[tex]\[ \frac{1}{9} \times 729 = \frac{729}{9} = 81 \][/tex]
So, [tex]\( f(3) = 81 \)[/tex].
Therefore, the correct answer is:
[tex]\[ \boxed{81} \][/tex]
