# Find the Domain y=1/( square root of x^2-4)

Find the Domain y=1/( square root of x^2-4)
Set the radicand in greater than or equal to to find where the expression is defined.
Since the left side has an even power, it is always positive for all real numbers.
All real numbers
Set the denominator in equal to to find where the expression is undefined.
Solve for .
Add to both sides of the equation.
To remove the radical on the left side of the equation, square both sides of the equation.
Simplify each side of the equation.
Multiply the exponents in .
Apply the power rule and multiply exponents, .
Multiply by .
Raise to the power of .
Solve for .
Take the square root of both sides of the equation 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.
The complete solution is the result of both the positive and negative portions of the solution.
The domain is all values of that make the expression defined.
Interval Notation:
Set-Builder Notation:
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