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The only problem with the domain comes from the square root. What numbers are you not able to take a square root of?
You can take the square root of those numbers. The roots will be irrational, but they exist. What numbers can you not take the square root of?
\(\sqrt 0 = 0\) since \(0^2 = 0\) 0 is still ok.
Is the answer negative numbers?
so its all real #s
Taking a square root is the opposite of squaring. Think of a negative number, such as -4. If you square 2, you get 4, not -4. If you square -2, you also get 4, not -4. There is no real number that you can square and get a negative number. This is because positive times positive is positive, and also negative times negative is positive.
When you deal with real numbers, there is no such thing as taking the square root of a negative number.
Your function has a square root. The expression inside the square rot cannot be negative. The domain of the function is all values that can be used for x. You can use any value of x as long as it does not cause the square root of a negative number.
Remember that square root of zero is zero, so it is real. We just cannot have the square root of a negative number. That means we can have the square root of all non-negative numbers.
so because of the square root in this case,its all numbers becuasue either way, the outcome will still be positive
No. Any value of x that will cause a negative number inside the root is not acceptable.
i clicked the wrong button
For example, look at x = 1. It causes the radicand to be negative. x = 1 must be excluded from the domain.
so its all numbers starting at 4 and above
Once again, the radicand must be non-negative. Non-negative means zero or positive. That means whatever is inside the root must be greater than or equal to zero.
You set the radicand equal to or greater than zero. Now you need to solve this inequality of x. The solution of this inequality is the domain of the function.
x greater or equal to 2
Do you know how to solve a quadratic inequality?
First, factor the left side.
i c where ur going
If this were an equation, the solutions would be -2 and 2. Since we have an inequality, we have a few more steps. The -2 and 2 are two points of interest for us. We put them on a number line.
We use closed dots at -2 and 2 because the inequality has a grater than or equal to sign, not just >.
The points -2 and 2 separate the number line into 3 different regions. Now we need to test each region to see which one or ones are the solutions to the inequality.
Let's test a point from the left of -2. Let's try -3. |dw:1450072111211:dw|
No. x^2 - 4 factors into (x + 2)(x - 2)
-3 makes the inequality true, so every point in the same region as -3 works. Now let's test 0. |dw:1450072220527:dw|
wait so what was the domain
0 does not work, so the region 0 is in does not work.
Now we test a point from the right region, to the right of 2. Let's test 3.
3 works, so all numbers in the region where 3 is also work.