Answer :
To find [tex]\( f(3) \)[/tex], we start by using the function provided:
[tex]\[ f(x) = \left(\frac{1}{7}\right)\left(7^x\right) \][/tex]
We need to calculate [tex]\( f(3) \)[/tex], which means we substitute [tex]\( x = 3 \)[/tex] into the function:
[tex]\[ f(3) = \left(\frac{1}{7}\right)\left(7^3\right) \][/tex]
Now, let's simplify step-by-step:
1. Calculate [tex]\( 7^3 \)[/tex], which means multiplying 7 by itself three times:
[tex]\( 7 \times 7 \times 7 = 343 \)[/tex]
2. Then, multiply this result by [tex]\(\frac{1}{7}\)[/tex]:
[tex]\(\frac{1}{7} \times 343 = \frac{343}{7}\)[/tex]
3. Finally, divide 343 by 7:
[tex]\( 343 \div 7 = 49 \)[/tex]
Therefore, [tex]\( f(3) = 49 \)[/tex].
So, the correct answer is [tex]\( \boxed{49} \)[/tex].
[tex]\[ f(x) = \left(\frac{1}{7}\right)\left(7^x\right) \][/tex]
We need to calculate [tex]\( f(3) \)[/tex], which means we substitute [tex]\( x = 3 \)[/tex] into the function:
[tex]\[ f(3) = \left(\frac{1}{7}\right)\left(7^3\right) \][/tex]
Now, let's simplify step-by-step:
1. Calculate [tex]\( 7^3 \)[/tex], which means multiplying 7 by itself three times:
[tex]\( 7 \times 7 \times 7 = 343 \)[/tex]
2. Then, multiply this result by [tex]\(\frac{1}{7}\)[/tex]:
[tex]\(\frac{1}{7} \times 343 = \frac{343}{7}\)[/tex]
3. Finally, divide 343 by 7:
[tex]\( 343 \div 7 = 49 \)[/tex]
Therefore, [tex]\( f(3) = 49 \)[/tex].
So, the correct answer is [tex]\( \boxed{49} \)[/tex].
