Answer :
To solve for [tex]\( f(3) \)[/tex] given the function [tex]\( f(x) = \left(\frac{1}{7}\right)\left(7^x\right) \)[/tex], follow these steps:
1. Substitute [tex]\( x = 3 \)[/tex] into the function:
Start with the function:
[tex]\[
f(x) = \left(\frac{1}{7}\right)\left(7^x\right)
\][/tex]
Replace [tex]\( x \)[/tex] with 3:
[tex]\[
f(3) = \left(\frac{1}{7}\right)\left(7^3\right)
\][/tex]
2. Calculate [tex]\( 7^3 \)[/tex]:
Multiply 7 by itself three times:
[tex]\[
7^3 = 7 \times 7 \times 7 = 343
\][/tex]
3. Multiply by [tex]\(\frac{1}{7}\)[/tex]:
Now multiply [tex]\(\frac{1}{7}\)[/tex] by 343:
[tex]\[
f(3) = \frac{1}{7} \times 343 = 49
\][/tex]
Therefore, the value of [tex]\( f(3) \)[/tex] is 49, which corresponds to option D.
1. Substitute [tex]\( x = 3 \)[/tex] into the function:
Start with the function:
[tex]\[
f(x) = \left(\frac{1}{7}\right)\left(7^x\right)
\][/tex]
Replace [tex]\( x \)[/tex] with 3:
[tex]\[
f(3) = \left(\frac{1}{7}\right)\left(7^3\right)
\][/tex]
2. Calculate [tex]\( 7^3 \)[/tex]:
Multiply 7 by itself three times:
[tex]\[
7^3 = 7 \times 7 \times 7 = 343
\][/tex]
3. Multiply by [tex]\(\frac{1}{7}\)[/tex]:
Now multiply [tex]\(\frac{1}{7}\)[/tex] by 343:
[tex]\[
f(3) = \frac{1}{7} \times 343 = 49
\][/tex]
Therefore, the value of [tex]\( f(3) \)[/tex] is 49, which corresponds to option D.
