Answer :
To find [tex]\( f(3) \)[/tex] for the function [tex]\( f(x) = \left(\frac{1}{7}\right) \left(7^x\right) \)[/tex], we need to plug in the value of 3 for [tex]\( x \)[/tex].
Here are the steps to solve the problem:
1. Start with the given function:
[tex]\[
f(x) = \left(\frac{1}{7}\right) \left(7^x\right)
\][/tex]
2. Substitute [tex]\( x = 3 \)[/tex] into the function:
[tex]\[
f(3) = \left(\frac{1}{7}\right) \left(7^3\right)
\][/tex]
3. Calculate [tex]\( 7^3 \)[/tex]:
[tex]\[
7^3 = 7 \times 7 \times 7 = 343
\][/tex]
4. Substitute [tex]\( 343 \)[/tex] for [tex]\( 7^3 \)[/tex] in the expression:
[tex]\[
f(3) = \left(\frac{1}{7}\right) \times 343
\][/tex]
5. Simplify the expression:
[tex]\[
f(3) = \frac{343}{7}
\][/tex]
6. Perform the division:
[tex]\[
\frac{343}{7} = 49
\][/tex]
Therefore, the answer is [tex]\( f(3) = 49 \)[/tex].
The correct choice from the options provided is:
A. 49
Here are the steps to solve the problem:
1. Start with the given function:
[tex]\[
f(x) = \left(\frac{1}{7}\right) \left(7^x\right)
\][/tex]
2. Substitute [tex]\( x = 3 \)[/tex] into the function:
[tex]\[
f(3) = \left(\frac{1}{7}\right) \left(7^3\right)
\][/tex]
3. Calculate [tex]\( 7^3 \)[/tex]:
[tex]\[
7^3 = 7 \times 7 \times 7 = 343
\][/tex]
4. Substitute [tex]\( 343 \)[/tex] for [tex]\( 7^3 \)[/tex] in the expression:
[tex]\[
f(3) = \left(\frac{1}{7}\right) \times 343
\][/tex]
5. Simplify the expression:
[tex]\[
f(3) = \frac{343}{7}
\][/tex]
6. Perform the division:
[tex]\[
\frac{343}{7} = 49
\][/tex]
Therefore, the answer is [tex]\( f(3) = 49 \)[/tex].
The correct choice from the options provided is:
A. 49
