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Video transcript

find the domain of f of X is equal to the principal square root of 2x minus 8 so the domain of a function is just the set of all of the possible valid inputs into the function or all of the possible values for which the function is defined and when we look at the how the function is defined right over here as the square root the principal square root of 2x minus 8 it's only going to be defined when it's taking the principal square root of a non-negative number and so 2x minus 8 2 X minus 8 it's only going to be defined when 2x minus 8 is greater than or equal to zero it can be zero because it you just take the square root of zero is zero it can be positive but if this was negative then all of a sudden this principal square root function which we're assuming is just the plain vanilla one for real numbers it would not be defined so this function definition is only defined when 2x minus 8 is greater than or equal to zero and then we could say what if 2x minus 8 has to be greater than or equal to zero we can solve this inequality to see what it's saying about what X has to be so if we add 8 to both sides of this inequality you get let me just add 8 to both sides you get these 8 to cancel out you get 2x is greater than or equal to 8 0 plus 8 is 8 and then you divide both sides by 2 since 2 is a positive number you don't have to swap the inequality so you divide both sides by 2 and you get X needs to be greater than or equal to 4 so the domain here is the set of all real numbers where that are greater than or equal to 4 X has to be greater than equal to 4 or in other words saying this function is defined when X is greater than equal to 4 and we're done