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Examples finding the domain of functions

CCSS.Math:

Video transcript

in this video we're gonna do a few examples finding domains of functions so let's say that we have the function f of X is equal to X plus 5 over X minus 2 what is going to be the domain of this function pause this video and try to figure that out all right now let's do it together now the domain is the set of all X values that if we input it into this function we're going to get a legitimate output we're going to get a legitimate f of X and so what's the situation where we would not get a legitimate f of X well if we input an x value that makes this denominator equal to 0 then we're going to divide by 0 and that's going to be undefined and so we could say the domain the domain here is all real values of X such that X minus 2 does not equal 0 now typically people would not want to just see that such that X minus 2 does not equal 0 and so we can simplify this a little bit so that we just have an X on the left hand side so if we add 2 to both sides of this we would get actually let me just do that let me add 2 to both sides so X minus 2 not equaling 0 is the same thing as X not equally two and you could have done that in your head as well if you wanted to keep X minus 2 from being 0 X just can't be equal to 2 and so typically people would say that the domain here is all real values of X such that X does not equal 2 let's do another example let's say that we're told that G of X is equal to the principal root of X minus 7 what's the domain in this situation what's the domain of G of X pause the video and try to figure that out well we could say that domain the domain is going to be all real values of X such that our we're going to have to put any constraints on this well when does a principal root function break down well if we tried to find the principal root the square root of a negative number well that would then break down and so X minus seven whatever we have under the radical here needs to be greater than or equal to zero so such that X minus seven needs to be greater than or equal to zero now another way to say that is we add 7 to both sides of that that would be saying that X needs to be greater than or equal to 7 so let me just write it that way so such that X is greater than or equal to 7 so all I did is I said all right where could this thing break down well if I get X values where this thing is negative we're in trouble so X needs to be greater X minus 7 whatever we have in this under the radical needs to be greater than or equal to zero and so if you say that X minus 7 needs to be greater than or equal to 0 you add 7 to both sides you get X needs to be greater than or equal to positive 7 let's do one last example let's say we're told that H of X is equal to X minus 5 squared what's the domain here so let me write this down the domain is all real values of X now are we going to have to constrain this a little bit well is there anything that would cause this to not evaluate to a defined value well we can square any value you to give me any real number and if I square it I'm gonna just getting another real number and so X minus 5 can be equal to anything and so X couldn't be equal to anything so here the domain is all real values of X we didn't have to constrain it in any way like we did the other two the other two when you deal with something in a denominator that could be equal to zero then you got to make sure that that doesn't happen because that would get you an undefined value and similarly for a radical you can't take the square root of a negative and so we would once again have to constrain on that