Question

What is the domain of the function?

`f(x) = (5)/(4x + 12)`

Answer 1

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) = (5)/(4c+12)`


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


`4x+12=0`


`x=-3`

(-\infty},-3) ∪ (-3,\infty})

Answer 2

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)`