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] at [tex]\( x = 3 \)[/tex].
Here are the steps to find [tex]\( f(3) \)[/tex]:
1. Identify the function: The given function is [tex]\( f(x) = \left(\frac{1}{7}\right)\left(7^x\right) \)[/tex].
2. Substitute the value of [tex]\( x \)[/tex]: We need to calculate [tex]\( f(3) \)[/tex]. This means we substitute [tex]\( x = 3 \)[/tex] into the function:
[tex]\[
f(3) = \left(\frac{1}{7}\right)\left(7^3\right)
\][/tex]
3. Calculate [tex]\( 7^3 \)[/tex]:
- [tex]\( 7 \times 7 = 49 \)[/tex]
- [tex]\( 49 \times 7 = 343 \)[/tex]
So, [tex]\( 7^3 = 343 \)[/tex].
4. Multiply by [tex]\(\frac{1}{7}\)[/tex]:
[tex]\[
f(3) = \left(\frac{1}{7}\right) \times 343
\][/tex]
5. Divide 343 by 7:
- [tex]\( 343 \div 7 = 49 \)[/tex]
Therefore, the value of [tex]\( f(3) \)[/tex] is 49.
The correct answer is:
D. 49
Here are the steps to find [tex]\( f(3) \)[/tex]:
1. Identify the function: The given function is [tex]\( f(x) = \left(\frac{1}{7}\right)\left(7^x\right) \)[/tex].
2. Substitute the value of [tex]\( x \)[/tex]: We need to calculate [tex]\( f(3) \)[/tex]. This means we substitute [tex]\( x = 3 \)[/tex] into the function:
[tex]\[
f(3) = \left(\frac{1}{7}\right)\left(7^3\right)
\][/tex]
3. Calculate [tex]\( 7^3 \)[/tex]:
- [tex]\( 7 \times 7 = 49 \)[/tex]
- [tex]\( 49 \times 7 = 343 \)[/tex]
So, [tex]\( 7^3 = 343 \)[/tex].
4. Multiply by [tex]\(\frac{1}{7}\)[/tex]:
[tex]\[
f(3) = \left(\frac{1}{7}\right) \times 343
\][/tex]
5. Divide 343 by 7:
- [tex]\( 343 \div 7 = 49 \)[/tex]
Therefore, the value of [tex]\( f(3) \)[/tex] is 49.
The correct answer is:
D. 49
