Answer :
To solve the problem, we need to find the value of the function [tex]\( f(x) = \left(\frac{1}{7}\right)\left(7^x\right) \)[/tex] when [tex]\( x = 3 \)[/tex].
Let's break it down step-by-step:
1. Substitute [tex]\( x = 3 \)[/tex] into the function [tex]\( f(x) \)[/tex]:
[tex]\[
f(3) = \left(\frac{1}{7}\right)\left(7^3\right)
\][/tex]
2. Calculate [tex]\( 7^3 \)[/tex]:
- [tex]\( 7^3 \)[/tex] means multiplying 7 by itself three times: [tex]\( 7 \times 7 \times 7 = 343 \)[/tex].
3. Multiply [tex]\( \frac{1}{7} \)[/tex] by 343:
- [tex]\[
f(3) = \left(\frac{1}{7}\right) \times 343 = \frac{343}{7}
\][/tex]
4. Calculate [tex]\( \frac{343}{7} \)[/tex]:
- Dividing 343 by 7 gives 49.
So, [tex]\( f(3) = 49 \)[/tex].
Therefore, the correct answer is D. 49.
Let's break it down step-by-step:
1. Substitute [tex]\( x = 3 \)[/tex] into the function [tex]\( f(x) \)[/tex]:
[tex]\[
f(3) = \left(\frac{1}{7}\right)\left(7^3\right)
\][/tex]
2. Calculate [tex]\( 7^3 \)[/tex]:
- [tex]\( 7^3 \)[/tex] means multiplying 7 by itself three times: [tex]\( 7 \times 7 \times 7 = 343 \)[/tex].
3. Multiply [tex]\( \frac{1}{7} \)[/tex] by 343:
- [tex]\[
f(3) = \left(\frac{1}{7}\right) \times 343 = \frac{343}{7}
\][/tex]
4. Calculate [tex]\( \frac{343}{7} \)[/tex]:
- Dividing 343 by 7 gives 49.
So, [tex]\( f(3) = 49 \)[/tex].
Therefore, the correct answer is D. 49.
