Precalculus Examples

Find the Domain x/( square root of x-6)
Step 1
Set the radicand in greater than or equal to to find where the expression is defined.
Step 2
Add to both sides of the inequality.
Step 3
Set the denominator in equal to to find where the expression is undefined.
Step 4
Solve for .
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Step 4.1
To remove the radical on the left side of the equation, square both sides of the equation.
Step 4.2
Simplify each side of the equation.
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Step 4.2.1
Use to rewrite as .
Step 4.2.2
Simplify the left side.
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Step 4.2.2.1
Simplify .
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Step 4.2.2.1.1
Multiply the exponents in .
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Step 4.2.2.1.1.1
Apply the power rule and multiply exponents, .
Step 4.2.2.1.1.2
Cancel the common factor of .
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Step 4.2.2.1.1.2.1
Cancel the common factor.
Step 4.2.2.1.1.2.2
Rewrite the expression.
Step 4.2.2.1.2
Simplify.
Step 4.2.3
Simplify the right side.
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Step 4.2.3.1
Raising to any positive power yields .
Step 4.3
Add to both sides of the equation.
Step 5
The domain is all values of that make the expression defined.
Interval Notation:
Set-Builder Notation:
Step 6