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Current time:0:00Total duration:2:38

Function notation — Harder example

Video transcript

let Y of X equal to the cube be equal to the cube root of x to the third plus one which of the following is equivalent to Y of Y of X all right this is going to be fun so we know that Y of X Y of X is equal to the cube root of x to the third plus one which of the following is equivalent to Y of Y of X well to evaluate Y of Y of X Y of Y of Y of X everywhere we see an X here we would just replace it with the Y with a Y of X it's kind of confuse Eve a little bit daunting because it's referring to itself but it should make all make sense in the end so we're gonna have something to the third power plus one and in this case that something is Y of X Y of X so what's Y of X equal to well it's equal to all of this business so let me write this down so this is going to be equal to this is going to be equal to the cube root of the cube root of give myself some space so Y of X is is the cube root of x to the third plus one now we're going to raise that to the third power and reset to the third power plus one and so we just have to evaluate this so what is this going to be well this is going to be the cube root the cube root of well what we have right over here if I have if I take the cube root of something but then I raise it to the third power this is like we raising something to the one third and then raising that to the third well that's just gonna give me this thing this all of this business right over here is just going to evaluate to X to the third plus one once again if I just take the cube root of something of whatever this is and then raise that to the third power that's going to be this original something maybe I should put a you know if I take the cube root of a and if I raised it to the third power that's just going to be a that's all I did right over here the cube root of x to the third plus one to the third power it's going to be X to the third plus one and then now we have the plus one so this is going to be equal to the cube root of x to the third plus two x to the third plus two which is that choice right over there