Answer :
To solve the problem and find [tex]\( f(3) \)[/tex] for the function [tex]\( f(x) = \left(\frac{1}{7}\right)\left(7^x\right) \)[/tex], follow these steps:
1. Understand the function:
The function is [tex]\( f(x) = \left(\frac{1}{7}\right)\left(7^x\right) \)[/tex]. Here, [tex]\( \frac{1}{7} \)[/tex] is a constant multiplier, and [tex]\( 7^x \)[/tex] represents an exponential function.
2. Substitute the given value:
We need to calculate [tex]\( f(3) \)[/tex], so we substitute [tex]\( x = 3 \)[/tex] into the function.
3. Perform the calculation:
- Calculate the exponential part: [tex]\( 7^3 \)[/tex]. This means multiplying 7 by itself three times:
[tex]\[
7^3 = 7 \times 7 \times 7 = 343
\][/tex]
- Multiply the result by the constant [tex]\( \frac{1}{7} \)[/tex]:
[tex]\[
f(3) = \frac{1}{7} \times 343 = 49
\][/tex]
4. Select the answer:
From the choices given:
- A. 343
- B. [tex]\(\frac{1}{343}\)[/tex]
- C. 49
- D. [tex]\(\frac{1}{49}\)[/tex]
The correct answer is [tex]\( \boxed{49} \)[/tex].
1. Understand the function:
The function is [tex]\( f(x) = \left(\frac{1}{7}\right)\left(7^x\right) \)[/tex]. Here, [tex]\( \frac{1}{7} \)[/tex] is a constant multiplier, and [tex]\( 7^x \)[/tex] represents an exponential function.
2. Substitute the given value:
We need to calculate [tex]\( f(3) \)[/tex], so we substitute [tex]\( x = 3 \)[/tex] into the function.
3. Perform the calculation:
- Calculate the exponential part: [tex]\( 7^3 \)[/tex]. This means multiplying 7 by itself three times:
[tex]\[
7^3 = 7 \times 7 \times 7 = 343
\][/tex]
- Multiply the result by the constant [tex]\( \frac{1}{7} \)[/tex]:
[tex]\[
f(3) = \frac{1}{7} \times 343 = 49
\][/tex]
4. Select the answer:
From the choices given:
- A. 343
- B. [tex]\(\frac{1}{343}\)[/tex]
- C. 49
- D. [tex]\(\frac{1}{49}\)[/tex]
The correct answer is [tex]\( \boxed{49} \)[/tex].
