Question

What is the domain of the function?
$f(x) = \frac{5}{4x + 12}$

Answer 1

The domain is always real numbers, unless x is in the denominator or under a square root. If that happens, whatever values make the denominator 0 are excluded from the domain. Or whatever values make the square root negative are excluded from the range.

4x + 12 = 0

4x = -12
x = -3

The domain is all real numbers except at x = -3.

x > -3 or x < -3

The domain written in interval notation is:
$(-\infty, 3)~ \cup ~(-3, \infty)$

Answer 2

Domain: The set of all possible input values (commonly the "x" variable) It is the set of all real numbers for which a function is mathematically defined. 

$f(x) = \frac{5}{4c+12}$ 

$x\ \textgreater \ -3$ or $x=\ \textless \ -3$ 

$4x+12=0$
 
$x=-3$

(-\infty},-3) ∪ (-3,\infty})