anonymous
  • anonymous
find the domain of the function
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
|dw:1450070862084:dw|
mathstudent55
  • mathstudent55
The only problem with the domain comes from the square root. What numbers are you not able to take a square root of?
anonymous
  • anonymous
5,7,13 ect

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mathstudent55
  • mathstudent55
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?
anonymous
  • anonymous
0
mathstudent55
  • mathstudent55
\(\sqrt 0 = 0\) since \(0^2 = 0\) 0 is still ok.
anonymous
  • anonymous
Is the answer negative numbers?
anonymous
  • anonymous
so its all real #s
mathstudent55
  • mathstudent55
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.
mathstudent55
  • mathstudent55
When you deal with real numbers, there is no such thing as taking the square root of a negative number.
mathstudent55
  • mathstudent55
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.
mathstudent55
  • mathstudent55
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.
anonymous
  • anonymous
so because of the square root in this case,its all numbers becuasue either way, the outcome will still be positive
mathstudent55
  • mathstudent55
No. Any value of x that will cause a negative number inside the root is not acceptable.
anonymous
  • anonymous
my bad
anonymous
  • anonymous
i clicked the wrong button
mathstudent55
  • mathstudent55
|dw:1450071429208:dw|
anonymous
  • anonymous
okay gotcha
mathstudent55
  • mathstudent55
For example, look at x = 1. It causes the radicand to be negative. x = 1 must be excluded from the domain.
anonymous
  • anonymous
so its all numbers starting at 4 and above
mathstudent55
  • mathstudent55
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.
mathstudent55
  • mathstudent55
|dw:1450071566185:dw|
mathstudent55
  • mathstudent55
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.
anonymous
  • anonymous
x greater or equal to 2
mathstudent55
  • mathstudent55
Do you know how to solve a quadratic inequality?
mathstudent55
  • mathstudent55
First, factor the left side.
anonymous
  • anonymous
|dw:1450071760561:dw|
anonymous
  • anonymous
ok
anonymous
  • anonymous
i c where ur going
mathstudent55
  • mathstudent55
|dw:1450071812323:dw|
mathstudent55
  • mathstudent55
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.
mathstudent55
  • mathstudent55
|dw:1450071886160:dw|
mathstudent55
  • mathstudent55
We use closed dots at -2 and 2 because the inequality has a grater than or equal to sign, not just >.
mathstudent55
  • mathstudent55
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.
anonymous
  • anonymous
ik wait
anonymous
  • anonymous
|dw:1450072074616:dw|
mathstudent55
  • mathstudent55
Let's test a point from the left of -2. Let's try -3. |dw:1450072111211:dw|
mathstudent55
  • mathstudent55
No. x^2 - 4 factors into (x + 2)(x - 2)
anonymous
  • anonymous
oh ok
mathstudent55
  • mathstudent55
-3 makes the inequality true, so every point in the same region as -3 works. Now let's test 0. |dw:1450072220527:dw|
anonymous
  • anonymous
wait so what was the domain
mathstudent55
  • mathstudent55
0 does not work, so the region 0 is in does not work.
anonymous
  • anonymous
|dw:1450072279882:dw|
mathstudent55
  • mathstudent55
Now we test a point from the right region, to the right of 2. Let's test 3.
mathstudent55
  • mathstudent55
|dw:1450072316337:dw|
mathstudent55
  • mathstudent55
3 works, so all numbers in the region where 3 is also work.
mathstudent55
  • mathstudent55
|dw:1450072378885:dw|