Answer :
Let's find [tex]\( f(3) \)[/tex] for the function [tex]\( f(x) = \left(\frac{1}{7}\right)\left(7^x\right) \)[/tex].
Step 1: Identify the function. The function is given by:
[tex]\[
f(x) = \left(\frac{1}{7}\right)\left(7^x\right)
\][/tex]
Step 2: Substitute [tex]\( x = 3 \)[/tex] into the function.
[tex]\[
f(3) = \left(\frac{1}{7}\right)\left(7^3\right)
\][/tex]
Step 3: Calculate [tex]\( 7^3 \)[/tex].
[tex]\[
7^3 = 7 \times 7 \times 7 = 343
\][/tex]
Step 4: Substitute this result back into the function.
[tex]\[
f(3) = \left(\frac{1}{7}\right) \times 343
\][/tex]
Step 5: Multiply [tex]\( \frac{1}{7} \)[/tex] by 343.
[tex]\[
\left(\frac{1}{7}\right) \times 343 = \frac{343}{7} = 49
\][/tex]
Therefore, the answer is [tex]\( f(3) = 49 \)[/tex].
The correct option is A. 49.
Step 1: Identify the function. The function is given by:
[tex]\[
f(x) = \left(\frac{1}{7}\right)\left(7^x\right)
\][/tex]
Step 2: Substitute [tex]\( x = 3 \)[/tex] into the function.
[tex]\[
f(3) = \left(\frac{1}{7}\right)\left(7^3\right)
\][/tex]
Step 3: Calculate [tex]\( 7^3 \)[/tex].
[tex]\[
7^3 = 7 \times 7 \times 7 = 343
\][/tex]
Step 4: Substitute this result back into the function.
[tex]\[
f(3) = \left(\frac{1}{7}\right) \times 343
\][/tex]
Step 5: Multiply [tex]\( \frac{1}{7} \)[/tex] by 343.
[tex]\[
\left(\frac{1}{7}\right) \times 343 = \frac{343}{7} = 49
\][/tex]
Therefore, the answer is [tex]\( f(3) = 49 \)[/tex].
The correct option is A. 49.
