Answer :
To solve the problem, we need to find the value of [tex]\( f(3) \)[/tex] using the given 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 of [tex]\( x \)[/tex] into the function:
We need to calculate [tex]\( f(3) \)[/tex], so replace [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]:
Find the value of [tex]\( 7^3 \)[/tex], which means multiplying 7 by itself twice:
[tex]\[
7^3 = 7 \times 7 \times 7 = 343
\][/tex]
3. Multiply by [tex]\(\frac{1}{7}\)[/tex]:
Now, take the result from the previous step and multiply it by [tex]\(\frac{1}{7}\)[/tex]:
[tex]\[
f(3) = \left(\frac{1}{7}\right)\times 343 = \frac{343}{7}
\][/tex]
4. Simplify the expression:
Divide 343 by 7:
[tex]\[
\frac{343}{7} = 49
\][/tex]
So, the value of [tex]\( f(3) \)[/tex] is 49.
The correct answer is D. 49.
Let's break it down step-by-step:
1. Substitute the value of [tex]\( x \)[/tex] into the function:
We need to calculate [tex]\( f(3) \)[/tex], so replace [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]:
Find the value of [tex]\( 7^3 \)[/tex], which means multiplying 7 by itself twice:
[tex]\[
7^3 = 7 \times 7 \times 7 = 343
\][/tex]
3. Multiply by [tex]\(\frac{1}{7}\)[/tex]:
Now, take the result from the previous step and multiply it by [tex]\(\frac{1}{7}\)[/tex]:
[tex]\[
f(3) = \left(\frac{1}{7}\right)\times 343 = \frac{343}{7}
\][/tex]
4. Simplify the expression:
Divide 343 by 7:
[tex]\[
\frac{343}{7} = 49
\][/tex]
So, the value of [tex]\( f(3) \)[/tex] is 49.
The correct answer is D. 49.
