Answer :
To find [tex]\( f(3) \)[/tex] for the function [tex]\( f(x) = \left(\frac{1}{7}\right)\left(7^x\right) \)[/tex], let's break it down step by step:
1. Substitute the value: We need to substitute [tex]\( x = 3 \)[/tex] into the function. This gives us:
[tex]\[
f(3) = \left(\frac{1}{7}\right)\left(7^3\right)
\][/tex]
2. Calculate [tex]\( 7^3 \)[/tex]: Calculate what 7 raised to the power of 3 is:
[tex]\[
7^3 = 7 \times 7 \times 7 = 343
\][/tex]
3. Multiply by [tex]\(\frac{1}{7}\)[/tex]: Now, multiply the result by [tex]\(\frac{1}{7}\)[/tex]:
[tex]\[
f(3) = \frac{1}{7} \times 343 = 49
\][/tex]
Therefore, the value of [tex]\( f(3) \)[/tex] is 49.
The correct answer is [tex]\( \boxed{49} \)[/tex].
1. Substitute the value: We need to substitute [tex]\( x = 3 \)[/tex] into the function. This gives us:
[tex]\[
f(3) = \left(\frac{1}{7}\right)\left(7^3\right)
\][/tex]
2. Calculate [tex]\( 7^3 \)[/tex]: Calculate what 7 raised to the power of 3 is:
[tex]\[
7^3 = 7 \times 7 \times 7 = 343
\][/tex]
3. Multiply by [tex]\(\frac{1}{7}\)[/tex]: Now, multiply the result by [tex]\(\frac{1}{7}\)[/tex]:
[tex]\[
f(3) = \frac{1}{7} \times 343 = 49
\][/tex]
Therefore, the value of [tex]\( f(3) \)[/tex] is 49.
The correct answer is [tex]\( \boxed{49} \)[/tex].
