Answer :
To solve for [tex]\( f(3) \)[/tex] in the function [tex]\( f(x) = \left(\frac{1}{7}\right)\left(7^x\right) \)[/tex], we need to substitute [tex]\( x \)[/tex] with 3 and simplify the expression.
Here's the step-by-step process:
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. Substitute [tex]\( 343 \)[/tex] back into the expression:
[tex]\[
f(3) = \left(\frac{1}{7}\right)(343)
\][/tex]
4. Simplify the expression by multiplying [tex]\( \frac{1}{7} \)[/tex] by [tex]\( 343 \)[/tex]:
[tex]\[
f(3) = \frac{343}{7}
\][/tex]
5. Perform the division:
[tex]\[
\frac{343}{7} = 49
\][/tex]
So, the value of [tex]\( f(3) \)[/tex] is [tex]\( 49 \)[/tex].
Therefore, the correct answer is B. 49.
Here's the step-by-step process:
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. Substitute [tex]\( 343 \)[/tex] back into the expression:
[tex]\[
f(3) = \left(\frac{1}{7}\right)(343)
\][/tex]
4. Simplify the expression by multiplying [tex]\( \frac{1}{7} \)[/tex] by [tex]\( 343 \)[/tex]:
[tex]\[
f(3) = \frac{343}{7}
\][/tex]
5. Perform the division:
[tex]\[
\frac{343}{7} = 49
\][/tex]
So, the value of [tex]\( f(3) \)[/tex] is [tex]\( 49 \)[/tex].
Therefore, the correct answer is B. 49.
