College

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. 343
D. [tex]\frac{1}{49}[/tex]

Answer :

We are given the function

[tex]$$
f(x) = \frac{1}{7} \cdot 7^x.
$$[/tex]

To find [tex]$f(3)$[/tex], substitute [tex]$3$[/tex] for [tex]$x$[/tex]:

[tex]$$
f(3) = \frac{1}{7} \cdot 7^3.
$$[/tex]

First, compute [tex]$7^3$[/tex]:

[tex]$$
7^3 = 7 \times 7 \times 7 = 343.
$$[/tex]

Now, substitute [tex]$343$[/tex] back into the expression:

[tex]$$
f(3) = \frac{1}{7} \cdot 343 = \frac{343}{7} = 49.
$$[/tex]

Thus, the value of [tex]$f(3)$[/tex] is [tex]$49$[/tex].