Answer :
Let's solve the problem step by step. We are given the function:
[tex]\[ f(x) = \left(\frac{1}{7}\right)\left(7^x\right) \][/tex]
and we need to find [tex]\( f(3) \)[/tex].
1. Substitute the value of [tex]\( x = 3 \)[/tex] into the function:
[tex]\[ f(3) = \left(\frac{1}{7}\right) \left(7^3\right) \][/tex]
2. Calculate [tex]\( 7^3 \)[/tex]:
[tex]\[ 7^3 = 7 \times 7 \times 7 = 343 \][/tex]
3. Multiply by [tex]\(\frac{1}{7}\)[/tex]:
[tex]\[ f(3) = \left(\frac{1}{7}\right) \times 343 = \frac{343}{7} \][/tex]
4. Divide [tex]\( 343 \)[/tex] by [tex]\( 7 \)[/tex]:
[tex]\[ \frac{343}{7} = 49 \][/tex]
So, the value of [tex]\( f(3) \)[/tex] is [tex]\( 49 \)[/tex].
Therefore, the correct answer is A. 49.
[tex]\[ f(x) = \left(\frac{1}{7}\right)\left(7^x\right) \][/tex]
and we need to find [tex]\( f(3) \)[/tex].
1. Substitute the value of [tex]\( x = 3 \)[/tex] into the function:
[tex]\[ f(3) = \left(\frac{1}{7}\right) \left(7^3\right) \][/tex]
2. Calculate [tex]\( 7^3 \)[/tex]:
[tex]\[ 7^3 = 7 \times 7 \times 7 = 343 \][/tex]
3. Multiply by [tex]\(\frac{1}{7}\)[/tex]:
[tex]\[ f(3) = \left(\frac{1}{7}\right) \times 343 = \frac{343}{7} \][/tex]
4. Divide [tex]\( 343 \)[/tex] by [tex]\( 7 \)[/tex]:
[tex]\[ \frac{343}{7} = 49 \][/tex]
So, the value of [tex]\( f(3) \)[/tex] is [tex]\( 49 \)[/tex].
Therefore, the correct answer is A. 49.
