To solve for [tex]\( f(3) \)[/tex] given the function [tex]\( f(x) = \left( \frac{1}{7} \right) (7^x) \)[/tex], let's follow these steps:
1. Substitute [tex]\( x \)[/tex] with 3 in the function [tex]\( f(x) \)[/tex]:
[tex]\[
f(3) = \left( \frac{1}{7} \right) (7^3)
\][/tex]
2. Calculate [tex]\( 7^3 \)[/tex]:
[tex]\[
7^3 = 7 \times 7 \times 7 = 343
\][/tex]
3. Multiply [tex]\( \frac{1}{7} \)[/tex] by [tex]\( 343 \)[/tex]:
[tex]\[
f(3) = \left( \frac{1}{7} \right) \times 343 = \frac{343}{7}
\][/tex]
4. Simplify [tex]\( \frac{343}{7} \)[/tex]:
[tex]\[
\frac{343}{7} = 49
\][/tex]
Thus, the value of [tex]\( f(3) \)[/tex] is [tex]\( 49 \)[/tex].
The correct answer is:
A. 49
