Answer :
To find [tex]\( f(3) \)[/tex] for the function [tex]\( f(x) = \left(\frac{1}{7}\right)\left(7^x\right) \)[/tex], we will plug in [tex]\( x = 3 \)[/tex] into the function and simplify.
Let's break it down step by step:
1. Substitute [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]\[
f(3) = \frac{1}{7} \times 343
\][/tex]
4. Simplify the multiplication:
To simplify [tex]\(\frac{1}{7} \times 343\)[/tex], we can perform the division:
[tex]\[
\frac{343}{7} = 49
\][/tex]
Therefore, the value of [tex]\( f(3) \)[/tex] is 49.
So the correct answer is:
C. 49
Let's break it down step by step:
1. Substitute [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]\[
f(3) = \frac{1}{7} \times 343
\][/tex]
4. Simplify the multiplication:
To simplify [tex]\(\frac{1}{7} \times 343\)[/tex], we can perform the division:
[tex]\[
\frac{343}{7} = 49
\][/tex]
Therefore, the value of [tex]\( f(3) \)[/tex] is 49.
So the correct answer is:
C. 49
