# Find the Domain y = natural log of x^2+3x-4

Set the argument in greater than to find where the expression is defined.
Solve for .
Convert the inequality to an equation.
Factor using the AC method.
Consider the form . Find a pair of integers whose product is and whose sum is . In this case, whose product is and whose sum is .
Write the factored form using these integers.
Set equal to and solve for .
Set the factor equal to .
Add to both sides of the equation.
Set equal to and solve for .
Set the factor equal to .
Subtract from both sides of the equation.
Consolidate the solutions.
Use each root to create test intervals.
Choose a test value from each interval and plug this value into the original inequality to determine which intervals satisfy the inequality.
Test a value on the interval to see if it makes the inequality true.
Choose a value on the interval and see if this value makes the original inequality true.
Replace with in the original inequality.
The left side is greater than the right side , which means that the given statement is always true.
True
True
Test a value on the interval to see if it makes the inequality true.
Choose a value on the interval and see if this value makes the original inequality true.
Replace with in the original inequality.
The left side is not greater than the right side , which means that the given statement is false.
False
False
Test a value on the interval to see if it makes the inequality true.
Choose a value on the interval and see if this value makes the original inequality true.
Replace with in the original inequality.
The left side is greater than the right side , which means that the given statement is always true.
True
True
Compare the intervals to determine which ones satisfy the original inequality.
True
False
True
True
False
True
The solution consists of all of the true intervals.
or
or
The domain is all values of that make the expression defined.
Interval Notation:
Set-Builder Notation:
Find the Domain y = natural log of x^2+3x-4