Exercises 123–125 will help you prepare for the material covered ...

Question

Exercises 123–125 will help you prepare for the material covered in the next section. Solve for y: x = y² -1, y ≥ 0.

Accepted Answer

Hello Today we're going to be taking our given expression and rewriting it as a function of Y. In terms of X. So the expression given to us is X equal to the square root of five minus Y cubed. Now in order to rewrite this as a function of Y. In terms of X, what that means is we want to go ahead and solve for our y variable. So we want to get our y variable by itself. Well in order to do that we need to first get this quantity out of the square root. And in order to do that we can go ahead and square both sides of the equation. Doing so is going to allow me to cancel the square root on the right hand side and it's going to square X. So what we are left with is X squared is equal to five minus y cubed. Now I want to go ahead and get y by itself but I need to get rid of this five first. What I can do is go ahead and subtract five to both sides of the equation and that's going to leave me with X squared minus five is equal to negative y cubed. Now I want to get rid of this negative So I'm gonna go ahead and divide everything by negative one and that's gonna give me positive y cubed is equal to positive five minus X squared now one more step I need to go ahead and get rid of this exponent of three. And in order to do that I can go ahead and take the cube root of both sides of the equation. And doing so is going to allow me to cancel out the exponent of three. And what I'm left with is why is equal to the cube root of the quantity five minus X squared. And this is going to be our function of Y in terms of X. And that means that the answer to this problem is going to be a. So I hope this video helps you understanding how to do this process and I'll go ahead and see you all in the next video.

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Exercises 123–125 will help you prepare for the material covered in the next section. Solve for y: x = y² -1, y ≥ 0.