Answer :
Let's solve the problem step by step:
We are given the function [tex]\( f(x) = \left(\frac{1}{7}\right)\left(7^x\right) \)[/tex] and asked to find [tex]\( f(3) \)[/tex].
1. Substitute 3 into the function:
Start by replacing [tex]\( x \)[/tex] with 3 in the function.
[tex]\[
f(3) = \left(\frac{1}{7}\right)\left(7^3\right)
\][/tex]
2. Calculate [tex]\( 7^3 \)[/tex]:
Calculate [tex]\( 7^3 \)[/tex], which means 7 multiplied by itself three times.
[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]\[
f(3) = \left(\frac{1}{7}\right) \times 343
\][/tex]
[tex]\[
f(3) = \frac{343}{7}
\][/tex]
4. Perform the division:
Divide 343 by 7 to simplify the expression.
[tex]\[
343 \div 7 = 49
\][/tex]
The final answer is [tex]\( f(3) = 49 \)[/tex].
Therefore, the correct choice is B. 49.
We are given the function [tex]\( f(x) = \left(\frac{1}{7}\right)\left(7^x\right) \)[/tex] and asked to find [tex]\( f(3) \)[/tex].
1. Substitute 3 into the function:
Start by replacing [tex]\( x \)[/tex] with 3 in the function.
[tex]\[
f(3) = \left(\frac{1}{7}\right)\left(7^3\right)
\][/tex]
2. Calculate [tex]\( 7^3 \)[/tex]:
Calculate [tex]\( 7^3 \)[/tex], which means 7 multiplied by itself three times.
[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]\[
f(3) = \left(\frac{1}{7}\right) \times 343
\][/tex]
[tex]\[
f(3) = \frac{343}{7}
\][/tex]
4. Perform the division:
Divide 343 by 7 to simplify the expression.
[tex]\[
343 \div 7 = 49
\][/tex]
The final answer is [tex]\( f(3) = 49 \)[/tex].
Therefore, the correct choice is B. 49.
