Precalculus Examples

Find the Domain 1/( square root of x-1)
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 .
Tap for more steps...
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.
Tap for more steps...
Step 4.2.1
Use to rewrite as .
Step 4.2.2
Simplify the left side.
Tap for more steps...
Step 4.2.2.1
Simplify .
Tap for more steps...
Step 4.2.2.1.1
Multiply the exponents in .
Tap for more steps...
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 .
Tap for more steps...
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.
Tap for more steps...
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