Answer :
To find [tex]\( f(3) \)[/tex] for the function [tex]\( f(x) = \left(\frac{1}{7}\right)\left(7^x\right) \)[/tex], we'll follow these steps:
1. Identify the Function: The function given is [tex]\( f(x) = \left(\frac{1}{7}\right)\left(7^x\right) \)[/tex].
2. Substitute [tex]\( x = 3 \)[/tex] into the Function:
- We replace [tex]\( x \)[/tex] with 3 in the function, which gives us:
[tex]\[
f(3) = \left(\frac{1}{7}\right)\left(7^3\right)
\][/tex]
3. Calculate [tex]\( 7^3 \)[/tex]:
- Calculate [tex]\( 7^3 \)[/tex], which is [tex]\( 7 \times 7 \times 7 = 343 \)[/tex].
4. Multiply by [tex]\( \frac{1}{7} \)[/tex]:
- Now, multiply [tex]\( 343 \)[/tex] by [tex]\(\frac{1}{7}\)[/tex]:
[tex]\[
\frac{1}{7} \times 343 = 49
\][/tex]
5. Conclusion:
- Therefore, [tex]\( f(3) = 49 \)[/tex].
So, the correct answer is [tex]\( D. \, 49 \)[/tex].
1. Identify the Function: The function given is [tex]\( f(x) = \left(\frac{1}{7}\right)\left(7^x\right) \)[/tex].
2. Substitute [tex]\( x = 3 \)[/tex] into the Function:
- We replace [tex]\( x \)[/tex] with 3 in the function, which gives us:
[tex]\[
f(3) = \left(\frac{1}{7}\right)\left(7^3\right)
\][/tex]
3. Calculate [tex]\( 7^3 \)[/tex]:
- Calculate [tex]\( 7^3 \)[/tex], which is [tex]\( 7 \times 7 \times 7 = 343 \)[/tex].
4. Multiply by [tex]\( \frac{1}{7} \)[/tex]:
- Now, multiply [tex]\( 343 \)[/tex] by [tex]\(\frac{1}{7}\)[/tex]:
[tex]\[
\frac{1}{7} \times 343 = 49
\][/tex]
5. Conclusion:
- Therefore, [tex]\( f(3) = 49 \)[/tex].
So, the correct answer is [tex]\( D. \, 49 \)[/tex].
