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Question 346763: y^2+x^2-4=0 . what is the domain and what is the range ?
Answer by haileytucki(390)   (Show Source):
You can put this solution on YOUR website! y^(2)+x^(2)-4=0
Move all terms not containing x to the right-hand side of the equation.
x^(2)=-y^(2)+4
Take the square root of both sides of the equation to eliminate the exponent on the left-hand side.
x=\~(-y^(2)+4)
First, substitute in the + portion of the \ to find the first solution.
x=~(-y^(2)+4)
Next, substitute in the - portion of the \ to find the second solution.
x=-~(-y^(2)+4)
The complete solution is the result of both the + and - portions of the solution.
x=~(-y^(2)+4),-~(-y^(2)+4)
The domain of an expression is all real numbers except for the regions where the expression is undefined. This can occur where the denominator equals 0, a square root is less than 0, or a logarithm is less than or equal to 0. All of these are undefined and therefore are not part of the domain.
(-y^(2)+4)<0
Solve the equation to find where the original expression is undefined.
No Solution
The domain of the rational expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.
All real numbers
The domain of the inverse of y^(2)+x^(2)-4=0 is equal to the range of f(y)=sqrt(-y^(2)+4).
Range: All real numbers
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