1
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Find the domain of f(x) is equal to the principal

2
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square root of 2x - 8

3
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So the domain of a function is just a set of all the possible

4
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valid inputs into the function

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or all of the possible values for which the function is defined

6
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And when we look at how the function is defined right over here

7
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It is a square root. The principal square root of 2x-8

8
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It's only going to be defined when its taking the principal square root of a non-negative number

9
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and so 2x-8 is only going to be defined when 2x-8 is greater than or equal to zero

10
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It can be zero because the square root of zero is zero

11
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It can be positive. But if this was negative then all of a sudden this principal

12
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square root function which we are just assuming is just the "plain vanilla" one

13
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for real numbers would not be defined

14
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So this function definition is only defined when 2x-8 is greater than or equal to zero

15
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and then we can say if 2x-8 has to be greater than or equal to zero we can solve this

16
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inequality to see what it is saying about what x has to be

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So if we add 8 to both sides of this inequality you get

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(these eights cancel out) you get 2x is greater than or equal to 8

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0 plus 8 is 8. And then you divide both sides by 2 since 2 is a positive number

20
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you don't have to swap the inequality. So you divide both sides by two

21
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and you get x needs to be greater than or equal to 4.

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So the domain here is the set of all real numbers that are greater than or equal to 4

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X has to be greater than or equal to 4

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and we are done!