Answer :
To solve the problem, we're given a function [tex]\( f(x) = \left(\frac{1}{7}\right)\left(7^x\right) \)[/tex] and we need to find [tex]\( f(3) \)[/tex].
Here's how we can do that step-by-step:
1. Substitute [tex]\( x = 3 \)[/tex] 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]:
Next, we need to calculate [tex]\( 7^3 \)[/tex]. This means multiplying 7 by itself three times:
[tex]\[
7^3 = 7 \times 7 \times 7 = 343
\][/tex]
3. Multiply by [tex]\(\frac{1}{7}\)[/tex]:
Now, we multiply 343 by [tex]\(\frac{1}{7}\)[/tex]:
[tex]\[
f(3) = \frac{343}{7} = 49
\][/tex]
So, [tex]\( f(3) = 49 \)[/tex].
The correct answer is D. 49.
Here's how we can do that step-by-step:
1. Substitute [tex]\( x = 3 \)[/tex] 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]:
Next, we need to calculate [tex]\( 7^3 \)[/tex]. This means multiplying 7 by itself three times:
[tex]\[
7^3 = 7 \times 7 \times 7 = 343
\][/tex]
3. Multiply by [tex]\(\frac{1}{7}\)[/tex]:
Now, we multiply 343 by [tex]\(\frac{1}{7}\)[/tex]:
[tex]\[
f(3) = \frac{343}{7} = 49
\][/tex]
So, [tex]\( f(3) = 49 \)[/tex].
The correct answer is D. 49.
