College

If [tex] f(x) = \left(\frac{1}{9}\right)\left(9^x\right) [/tex], what is [tex] f(3) [/tex]?

A. 729
B. [tex] \frac{1}{81} [/tex]
C. [tex] \frac{1}{729} [/tex]
D. 81

Answer :

To solve the problem, we are given a function [tex]\( f(x) = \frac{1}{9} \times 9^x \)[/tex] and need to find [tex]\( f(3) \)[/tex]. Here's a step-by-step breakdown:

1. Identify the Function: The function is specified as [tex]\( f(x) = \frac{1}{9} \times 9^x \)[/tex].

2. Substitute [tex]\( x = 3 \)[/tex] into the Function: We want to find the value of the function when [tex]\( x = 3 \)[/tex]. So, we substitute 3 into the equation:

[tex]\[
f(3) = \frac{1}{9} \times 9^3
\][/tex]

3. Calculate [tex]\( 9^3 \)[/tex]: First, we need to find [tex]\( 9^3 \)[/tex], which is:

[tex]\[
9^3 = 9 \times 9 \times 9
\][/tex]

Multiply step-by-step:

- [tex]\( 9 \times 9 = 81 \)[/tex]
- [tex]\( 81 \times 9 = 729 \)[/tex]

So, [tex]\( 9^3 = 729 \)[/tex].

4. Evaluate the Expression: Next, plug [tex]\( 9^3 \)[/tex] into the expression:

[tex]\[
f(3) = \frac{1}{9} \times 729
\][/tex]

5. Simplify the Expression: Simplify the multiplication:

[tex]\[
f(3) = \frac{729}{9}
\][/tex]

Divide 729 by 9:

- 729 divided by 9 equals 81

So, [tex]\( f(3) = 81 \)[/tex].

6. Conclusion: The value of [tex]\( f(3) \)[/tex] is 81. Therefore, the correct answer is:

D. 81

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