Question

find the domain of the function, $y = \log_{4}(7 - x)$
select one:
a. $(-\infty, \infty)$
b. $(7, \infty)$
c. $(4, \infty)$
d. $(-\infty, 7)$

Explanation:

Step1: Set argument > 0

For logarithm $\log_b(x)$, $x>0$. So:
$7 - x > 0$

Step2: Solve inequality for $x$

Rearrange to isolate $x$:
$x < 7$
This translates to the interval $(-\infty, 7)$.

Answer:

D. $(-\infty,7)$