Answer :
To find [tex]\( f(3) \)[/tex] for the function [tex]\( f(x) = \left(\frac{1}{7}\right)\left(7^x\right) \)[/tex], follow these steps:
1. Substitute the value into the function: We need to find [tex]\( f(3) \)[/tex], which means substituting [tex]\( x = 3 \)[/tex] into the function.
[tex]\[
f(3) = \left(\frac{1}{7}\right)\left(7^3\right)
\][/tex]
2. Calculate the power of 7: First, compute [tex]\( 7^3 \)[/tex].
[tex]\[
7^3 = 7 \times 7 \times 7 = 343
\][/tex]
3. Multiply by the fraction: Now, multiply the result by [tex]\( \frac{1}{7} \)[/tex].
[tex]\[
f(3) = \left(\frac{1}{7}\right) \times 343 = \frac{343}{7}
\][/tex]
4. Divide 343 by 7: Perform the division.
[tex]\[
\frac{343}{7} = 49
\][/tex]
So, the value of [tex]\( f(3) \)[/tex] is [tex]\( 49 \)[/tex]. Therefore, the answer is C. 49.
1. Substitute the value into the function: We need to find [tex]\( f(3) \)[/tex], which means substituting [tex]\( x = 3 \)[/tex] into the function.
[tex]\[
f(3) = \left(\frac{1}{7}\right)\left(7^3\right)
\][/tex]
2. Calculate the power of 7: First, compute [tex]\( 7^3 \)[/tex].
[tex]\[
7^3 = 7 \times 7 \times 7 = 343
\][/tex]
3. Multiply by the fraction: Now, multiply the result by [tex]\( \frac{1}{7} \)[/tex].
[tex]\[
f(3) = \left(\frac{1}{7}\right) \times 343 = \frac{343}{7}
\][/tex]
4. Divide 343 by 7: Perform the division.
[tex]\[
\frac{343}{7} = 49
\][/tex]
So, the value of [tex]\( f(3) \)[/tex] is [tex]\( 49 \)[/tex]. Therefore, the answer is C. 49.
