Graphing the inverse of a linear function

this right over here is our understanding inverses of functions exercise on Khan Academy and it's a good exercise to make sure you understand inverses of functions and it's an interactive one where we can we can move this line around and they tell us the graph of H of X is in green so that's this dotted blue green line right over here is the graph of H of X is the green dashed line segment shown below so that's this drag the end points of the segment below to graph H inverse of X so there's a couple of ways to tackle it perhaps the simplest one is we say okay look H of X how does what is H of X map from and to so H of X this point shows that H of X if you input negative 8 into H of X H of negative 8 is 1 so it's mapping from negative 8 to 1 well the inverse of that then should map from 1 to negative 8 it should map from 1 to negative 8 so let's put that point on the graph of the inverse and then let's go on the other end so let me just move this a little bit out of the way on the other end of H of X we see that when you input 3 into H of X when X is equal to 3 H of X is equal to negative 4 so this point shows us that its mapping from 3 to negative 4 so the universe of that would map from negative 4 to 3 so if you input negative 4 it should output 3 if you input negative 4 it should outpoint output 3 and since we took the two endpoints of this line and we essentially found the inverse mapping of it what I've just done here is I've graphed the inverse and another way to think about the inverse is if you were to draw the line y equals x so I don't have my my little pen tool right here because I'm operating on a webpage but if you imagine the line y equals x these things should be reflections around the line y equal X because one way to think about it is you're swapping the X's for the Y's over here and you see that if you were to draw the line y equals x these things this if you flipped it around the line y equals x 2 green line you would actually get the yellow line this would flip over there and this would flip over there but either way we're done we have graphed H inverse of X