The problem in the book is x 2 +(y-1) 2 =4 Is Y a function of x? The solution sa

Question

The problem in the book is x2+(y-1)2=4 Is Y a function of x? The solution says no because it factored (y-1)2 and got 2 solutions for Y. However, why cant I take the square root of both sides and get x+y-1=2 and y=3-x (so that y has one solution and is a function of x)? The problem in the book is x2+(y-1)2=4 Is Y a function of x? The solution says no because it factored (y-1)2 and got 2 solutions for Y. However, why cant I take the square root of both sides and get x+y-1=2 and y=3-x (so that y has one solution and is a function of x)?

Explanation / Answer

If you take the square root of both sides it will not give you the answer that you have stated. You have to take the square root of the entire left side if you want to take the square root of it. You can't just take the square root of each individual part.

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