Answer :
To solve the problem of finding [tex]\( f(3) \)[/tex] for the function [tex]\( f(x) = \left(\frac{1}{7}\right)\left(7^x\right) \)[/tex], we will follow these steps:
1. Substitute [tex]\( x \)[/tex] in the function with 3:
This means we need to calculate [tex]\( f(3) \)[/tex].
2. Evaluate the expression:
The function is given as [tex]\( f(x) = \left(\frac{1}{7}\right)\left(7^x\right) \)[/tex].
Substitute 3 for [tex]\( x \)[/tex]: [tex]\( f(3) = \left(\frac{1}{7}\right)\left(7^3\right) \)[/tex].
3. Calculate [tex]\( 7^3 \)[/tex]:
[tex]\( 7^3 = 7 \times 7 \times 7 = 343 \)[/tex].
4. Multiply by [tex]\( \frac{1}{7} \)[/tex]:
Since we have [tex]\( f(3) = \frac{1}{7} \times 343 \)[/tex], we will divide 343 by 7.
5. Division:
[tex]\( 343 \div 7 = 49 \)[/tex].
So, after performing these calculations, we find that [tex]\( f(3) = 49 \)[/tex].
Therefore, the answer is A. 49.
1. Substitute [tex]\( x \)[/tex] in the function with 3:
This means we need to calculate [tex]\( f(3) \)[/tex].
2. Evaluate the expression:
The function is given as [tex]\( f(x) = \left(\frac{1}{7}\right)\left(7^x\right) \)[/tex].
Substitute 3 for [tex]\( x \)[/tex]: [tex]\( f(3) = \left(\frac{1}{7}\right)\left(7^3\right) \)[/tex].
3. Calculate [tex]\( 7^3 \)[/tex]:
[tex]\( 7^3 = 7 \times 7 \times 7 = 343 \)[/tex].
4. Multiply by [tex]\( \frac{1}{7} \)[/tex]:
Since we have [tex]\( f(3) = \frac{1}{7} \times 343 \)[/tex], we will divide 343 by 7.
5. Division:
[tex]\( 343 \div 7 = 49 \)[/tex].
So, after performing these calculations, we find that [tex]\( f(3) = 49 \)[/tex].
Therefore, the answer is A. 49.
