Question

Can someone please tell me why it is x≤-4 instead of x≥-4. (File attached)

Answer 1

Because it means the same thing no matter which way it points.

Answer 2

um no it doesnt

Answer 3

It's because if x = 4, then the denominator would equal zero, which would be undefined. It is less than -4 because if you plug in a number less than -4 (ex. -5), then you would get a negative number in the radical, which is not a real number.

Answer 4

i still dont get it but thanks anyways

Answer 5

The denominator is the square root of x+4. If you plug in -5, for example, you would get...\[\sqrt{-5+4}\]\[\sqrt{-1}\]which is impossible because you can't have the square root of a negative number, since any negative number times another negative number is positive (when you square a number you're multiplying the same number by itself, so if it's a negative number, two negatives will equal a positive).

If the number was greater than -4, such as -3, then you would get...\[\sqrt{-3+4}\]which simplifies to \[\sqrt{1}\] which is just 1, so answers above -4 could potentially work if you were looking only at the denominator.

Answer 6

You might be getting confused because this problem works with negative numbers.
Numbers that fit into x<-4 include -5, -6, -7, -8, and so on because it's going toward negative infinity.
Numbers that fit into x>-4 include -3, -2, -1, 0, 1, and so on because it's going toward infinity.

Answer 7

so are you saying that the correct answer should be x>-4

Answer 8

?

Answer 9

Yeah.. except I just realized that that doesn't match with the answer given, but if I had to solve it the answer would be x>2.

Answer 10

x>=2*

Answer 11

yeah the answer is confusing me because idk how to state the domain -_-

Answer 12

I don't know... It's weird because it states the answer in interval form, but that's not the right answer...

Answer 13

oh ok so u dont know what the domain would be?

Answer 14

The domain should be \[(2,\infty)\]I don't see how it would be the answer given...

Answer 15

I mean... [2,∞) I forgot to include 2.

Answer 16

Domain of \[\Large \sqrt{x+4}\]


Radicand must be nonnegative, so \[\Large x+4 \ge0\]


\[\Large x \ge-4\]


So domain of \[\Large \sqrt{x+4}\] is \[\Large x \ge-4\]

Answer 17

That's why it's \[\Large x\ge -4\] instead of \[\Large x \le -4\]

Answer 18

@jim, it says the opposite answer it says the answer is x<=-4, not the other way around.

Answer 19

but the domain of sqrt(x+4) is not x <= -4

Answer 20

I know, that's why smurfy is confused.

Answer 21

well idk then, there must be a typo somewhere