# Find the Domain and Range square root of 4-x^2

Set the radicand in greater than or equal to to find where the expression is defined.
Solve for .
Subtract from both sides of the inequality.
Multiply each term in by
Multiply each term in by . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.
Multiply .
Multiply by .
Multiply by .
Multiply by .
Take the square root of both sides of the inequality to eliminate the exponent on the left side.
The complete solution is the result of both the positive and negative portions of the solution.
Simplify the right side of the equation.
Rewrite as .
Pull terms out from under the radical, assuming positive real numbers.
The complete solution is the result of both the positive and negative portions of the solution.
First, use the positive value of the to find the first solution.
Next, use the negative value of the to find the second solution. Since this is an inequality, flip the direction of the inequality sign on the portion of the solution.
The complete solution is the result of both the positive and negative portions of the solution.
and
Find the intersection.
The domain is all values of that make the expression defined.
Interval Notation:
Set-Builder Notation:
The range is the set of all valid values.
Interval Notation:
Set-Builder Notation:
Determine the domain and range.
Domain:
Range:
Find the Domain and Range square root of 4-x^2