Answer :
Sure! Let's solve the problem step-by-step to find the value of [tex]\( f(3) \)[/tex].
We have the function [tex]\( f(x) = \left(\frac{1}{7}\right)\left(7^x\right) \)[/tex].
To find [tex]\( f(3) \)[/tex], we'll follow these steps:
1. Substitute 3 in place of [tex]\( x \)[/tex]:
[tex]\[
f(3) = \left(\frac{1}{7}\right)\left(7^3\right)
\][/tex]
2. Calculate [tex]\( 7^3 \)[/tex]:
[tex]\[
7^3 = 7 \times 7 \times 7 = 343
\][/tex]
3. Multiply the result by [tex]\( \frac{1}{7} \)[/tex]:
[tex]\[
f(3) = \frac{1}{7} \times 343
\][/tex]
4. Divide 343 by 7:
[tex]\[
\frac{1}{7} \times 343 = 49
\][/tex]
Therefore, the value of [tex]\( f(3) \)[/tex] is 49.
So, the answer is [tex]\( \boxed{49} \)[/tex] which corresponds to option D.
We have the function [tex]\( f(x) = \left(\frac{1}{7}\right)\left(7^x\right) \)[/tex].
To find [tex]\( f(3) \)[/tex], we'll follow these steps:
1. Substitute 3 in place of [tex]\( x \)[/tex]:
[tex]\[
f(3) = \left(\frac{1}{7}\right)\left(7^3\right)
\][/tex]
2. Calculate [tex]\( 7^3 \)[/tex]:
[tex]\[
7^3 = 7 \times 7 \times 7 = 343
\][/tex]
3. Multiply the result by [tex]\( \frac{1}{7} \)[/tex]:
[tex]\[
f(3) = \frac{1}{7} \times 343
\][/tex]
4. Divide 343 by 7:
[tex]\[
\frac{1}{7} \times 343 = 49
\][/tex]
Therefore, the value of [tex]\( f(3) \)[/tex] is 49.
So, the answer is [tex]\( \boxed{49} \)[/tex] which corresponds to option D.
