Answer: Choice E
[tex]x \ne -4, -1[/tex]
This is the same as saying [tex]x \ne -4 \text{ and } x \ne -1[/tex]
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Reason:
If we plugged x = -4 into the function, then the x+4 in the denominator turns to 0.
x+4 = -4+4 = 0
Dividing by zero is not allowed. It leads to a division by zero error. Therefore, we need to exclude -4 from the domain. Similar reasoning will exclude -1 as well because it makes the x+1 in the denominator to be zero.
Any other x value is valid.
Side note: The (x+1) terms cancel, which may appear that x = -1 is valid. However, your calculator will likely not perform such a simplification. It will simply try to directly compute the result using PEMDAS. That means x = -1 is likely to produce a division by zero error.
