Answer :
Sure, 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]
We need to find [tex]\( f(3) \)[/tex].
Substitute [tex]\( x = 3 \)[/tex] into the function:
[tex]\[ f(3) = \left( \frac{1}{7} \right) \left( 7^3 \right) \][/tex]
Now, let's calculate [tex]\( 7^3 \)[/tex]:
[tex]\[ 7^3 = 7 \times 7 \times 7 = 343 \][/tex]
Next, we multiply this result by [tex]\( \frac{1}{7} \)[/tex]:
[tex]\[ f(3) = \left( \frac{1}{7} \right) \left( 343 \right) \][/tex]
To do this multiplication:
[tex]\[ f(3) = \frac{343}{7} \][/tex]
Perform the division:
[tex]\[ \frac{343}{7} = 49 \][/tex]
So, the value of [tex]\( f(3) \)[/tex] is:
[tex]\[ f(3) = 49 \][/tex]
Therefore, the correct answer is:
[tex]\[ \boxed{49} \][/tex]
We are given the function:
[tex]\[ f(x) = \left( \frac{1}{7} \right) \left( 7^x \right) \][/tex]
We need to find [tex]\( f(3) \)[/tex].
Substitute [tex]\( x = 3 \)[/tex] into the function:
[tex]\[ f(3) = \left( \frac{1}{7} \right) \left( 7^3 \right) \][/tex]
Now, let's calculate [tex]\( 7^3 \)[/tex]:
[tex]\[ 7^3 = 7 \times 7 \times 7 = 343 \][/tex]
Next, we multiply this result by [tex]\( \frac{1}{7} \)[/tex]:
[tex]\[ f(3) = \left( \frac{1}{7} \right) \left( 343 \right) \][/tex]
To do this multiplication:
[tex]\[ f(3) = \frac{343}{7} \][/tex]
Perform the division:
[tex]\[ \frac{343}{7} = 49 \][/tex]
So, the value of [tex]\( f(3) \)[/tex] is:
[tex]\[ f(3) = 49 \][/tex]
Therefore, the correct answer is:
[tex]\[ \boxed{49} \][/tex]
