Answer :
To find [tex]\( f(3) \)[/tex] for the function [tex]\( f(x) = \left(\frac{1}{7}\right)\left(7^x\right) \)[/tex], we will follow these steps:
1. Substitute the value of [tex]\( x \)[/tex] into the function
- We need to find [tex]\( f(3) \)[/tex], so we'll substitute 3 for [tex]\( x \)[/tex] in the equation [tex]\( f(x) = \left(\frac{1}{7}\right)\left(7^x\right) \)[/tex].
2. Calculate [tex]\( 7^3 \)[/tex]
- First, evaluate [tex]\( 7^3 \)[/tex], which means multiplying 7 by itself three times:
[tex]\[
7^3 = 7 \times 7 \times 7 = 343
\][/tex]
3. Multiply by [tex]\(\frac{1}{7}\)[/tex]
- Next, multiply [tex]\( 343 \)[/tex] by [tex]\(\frac{1}{7}\)[/tex]:
[tex]\[
\left(\frac{1}{7}\right) \times 343 = 49
\][/tex]
Thus, the value of [tex]\( f(3) \)[/tex] is [tex]\(\boxed{49}\)[/tex].
Therefore, the correct answer is:
A. 49
1. Substitute the value of [tex]\( x \)[/tex] into the function
- We need to find [tex]\( f(3) \)[/tex], so we'll substitute 3 for [tex]\( x \)[/tex] in the equation [tex]\( f(x) = \left(\frac{1}{7}\right)\left(7^x\right) \)[/tex].
2. Calculate [tex]\( 7^3 \)[/tex]
- First, evaluate [tex]\( 7^3 \)[/tex], which means multiplying 7 by itself three times:
[tex]\[
7^3 = 7 \times 7 \times 7 = 343
\][/tex]
3. Multiply by [tex]\(\frac{1}{7}\)[/tex]
- Next, multiply [tex]\( 343 \)[/tex] by [tex]\(\frac{1}{7}\)[/tex]:
[tex]\[
\left(\frac{1}{7}\right) \times 343 = 49
\][/tex]
Thus, the value of [tex]\( f(3) \)[/tex] is [tex]\(\boxed{49}\)[/tex].
Therefore, the correct answer is:
A. 49
