High School

If [tex]f(x)=\left(\frac{1}{7}\right)\left(7^x\right)[/tex], what is [tex]f(3)[/tex]?



A. 49

B. [tex]\frac{1}{343}[/tex]

C. [tex]\frac{1}{49}[/tex]

D. 343

Answer :

We are given the function

$$
f(x)=\frac{1}{7}\cdot 7^x.
$$

To find $f(3)$, substitute $x=3$ into the function:

$$
f(3)=\frac{1}{7}\cdot 7^3.
$$

First, calculate $7^3$:

$$
7^3 = 7\times7\times7 = 343.
$$

Now, substitute this back into the function:

$$
f(3)=\frac{1}{7}\cdot 343 = \frac{343}{7}.
$$

Divide $343$ by $7$:

$$
\frac{343}{7} = 49.
$$

Thus, the value of $f(3)$ is $49$.