To find [tex]\( f(3) \)[/tex] for the function [tex]\( f(x) = \left(\frac{1}{7}\right)\left(7^x\right) \)[/tex], we need to substitute [tex]\( x = 3 \)[/tex] into the given function and evaluate it.
Here's a step-by-step solution:
1. Write down the function:
[tex]\[
f(x) = \left(\frac{1}{7}\right) \left(7^x\right)
\][/tex]
2. Substitute [tex]\( x = 3 \)[/tex] into the function:
[tex]\[
f(3) = \left(\frac{1}{7}\right) \left(7^3\right)
\][/tex]
3. Simplify the exponentiation part:
[tex]\[
7^3 = 343
\][/tex]
4. Substitute [tex]\( 343 \)[/tex] back into the expression:
[tex]\[
f(3) = \left(\frac{1}{7}\right) \left(343\right)
\][/tex]
5. Perform the multiplication:
[tex]\[
\left(\frac{1}{7}\right) \left(343\right) = \frac{343}{7}
\][/tex]
6. Simplify the division:
[tex]\[
\frac{343}{7} = 49
\][/tex]
Thus, the value of [tex]\( f(3) \)[/tex] is:
[tex]\[
f(3) = 49
\][/tex]
