High School

If [tex]f(x)=\left(\frac{1}{5}\right)9^{x}[/tex], what is [tex]f(3)[/tex]?

A. 729
B. [tex]\frac{1}{128}[/tex]
C. 81
D. 0.1

Answer :

Certainly! Let's solve this step-by-step:

We're given a function:
[tex]\[ f(x) = \left(\frac{1}{5}\right) \times 9^x \][/tex]

We need to find the value of [tex]\( f(3) \)[/tex].

1. Calculate [tex]\( 9^3 \)[/tex]:

To do this, multiply 9 by itself three times:
[tex]\[
9^3 = 9 \times 9 \times 9 = 729
\][/tex]

2. Multiply by [tex]\(\frac{1}{5}\)[/tex]:

Now that we have [tex]\( 9^3 = 729 \)[/tex], we multiply it by [tex]\(\frac{1}{5}\)[/tex]:
[tex]\[
f(3) = \left(\frac{1}{5}\right) \times 729 = \frac{729}{5} = 145.8
\][/tex]

Based on our calculations:

- [tex]\( f(3) \)[/tex] is equal to 145.8.

In the context of the choices provided in the question, none of the options exactly matches this answer.
- The closest option does not exist, so it seems there may be a mismatch or error in the choices given.