Answer :
To solve the problem, we need to evaluate the function [tex]\( f(x) = \left(\frac{1}{7}\right)\left(7^x\right) \)[/tex] for [tex]\( x = 3 \)[/tex].
1. Start with the expression for the function:
[tex]\[
f(x) = \left(\frac{1}{7}\right) \times \left(7^x\right)
\][/tex]
2. Substitute [tex]\( x = 3 \)[/tex] into the function:
[tex]\[
f(3) = \left(\frac{1}{7}\right) \times \left(7^3\right)
\][/tex]
3. Calculate [tex]\( 7^3 \)[/tex]:
[tex]\[
7^3 = 7 \times 7 \times 7 = 49 \times 7 = 343
\][/tex]
4. Substitute [tex]\( 343 \)[/tex] back into the expression:
[tex]\[
f(3) = \left(\frac{1}{7}\right) \times 343
\][/tex]
5. Simplify the multiplication:
[tex]\[
f(3) = \frac{343}{7}
\][/tex]
6. Divide 343 by 7:
[tex]\[
343 \div 7 = 49
\][/tex]
Therefore, the value of [tex]\( f(3) \)[/tex] is [tex]\( 49 \)[/tex].
So the correct answer is [tex]\( \boxed{49} \)[/tex] which corresponds to option D.
1. Start with the expression for the function:
[tex]\[
f(x) = \left(\frac{1}{7}\right) \times \left(7^x\right)
\][/tex]
2. Substitute [tex]\( x = 3 \)[/tex] into the function:
[tex]\[
f(3) = \left(\frac{1}{7}\right) \times \left(7^3\right)
\][/tex]
3. Calculate [tex]\( 7^3 \)[/tex]:
[tex]\[
7^3 = 7 \times 7 \times 7 = 49 \times 7 = 343
\][/tex]
4. Substitute [tex]\( 343 \)[/tex] back into the expression:
[tex]\[
f(3) = \left(\frac{1}{7}\right) \times 343
\][/tex]
5. Simplify the multiplication:
[tex]\[
f(3) = \frac{343}{7}
\][/tex]
6. Divide 343 by 7:
[tex]\[
343 \div 7 = 49
\][/tex]
Therefore, the value of [tex]\( f(3) \)[/tex] is [tex]\( 49 \)[/tex].
So the correct answer is [tex]\( \boxed{49} \)[/tex] which corresponds to option D.
