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Linear Algebra Examples
Step 1
Set the radicand in greater than or equal to to find where the expression is defined.
Step 2
Step 2.1
To remove the radical on the left side of the inequality, cube both sides of the inequality.
Step 2.2
Simplify each side of the inequality.
Step 2.2.1
Use to rewrite as .
Step 2.2.2
Simplify the left side.
Step 2.2.2.1
Simplify .
Step 2.2.2.1.1
Apply the product rule to .
Step 2.2.2.1.2
Rewrite using the commutative property of multiplication.
Step 2.2.2.1.3
Multiply by by adding the exponents.
Step 2.2.2.1.3.1
Move .
Step 2.2.2.1.3.2
Multiply by .
Step 2.2.2.1.3.2.1
Raise to the power of .
Step 2.2.2.1.3.2.2
Use the power rule to combine exponents.
Step 2.2.2.1.3.3
Write as a fraction with a common denominator.
Step 2.2.2.1.3.4
Combine the numerators over the common denominator.
Step 2.2.2.1.3.5
Add and .
Step 2.2.2.1.4
Use the power rule to distribute the exponent.
Step 2.2.2.1.4.1
Apply the product rule to .
Step 2.2.2.1.4.2
Apply the product rule to .
Step 2.2.2.1.5
Raise to the power of .
Step 2.2.2.1.6
Multiply the exponents in .
Step 2.2.2.1.6.1
Apply the power rule and multiply exponents, .
Step 2.2.2.1.6.2
Cancel the common factor of .
Step 2.2.2.1.6.2.1
Cancel the common factor.
Step 2.2.2.1.6.2.2
Rewrite the expression.
Step 2.2.2.1.7
Evaluate the exponent.
Step 2.2.2.1.8
Multiply by .
Step 2.2.2.1.9
Multiply the exponents in .
Step 2.2.2.1.9.1
Apply the power rule and multiply exponents, .
Step 2.2.2.1.9.2
Cancel the common factor of .
Step 2.2.2.1.9.2.1
Cancel the common factor.
Step 2.2.2.1.9.2.2
Rewrite the expression.
Step 2.2.3
Simplify the right side.
Step 2.2.3.1
Raising to any positive power yields .
Step 2.3
Solve for .
Step 2.3.1
Divide each term in by and simplify.
Step 2.3.1.1
Divide each term in by .
Step 2.3.1.2
Simplify the left side.
Step 2.3.1.2.1
Cancel the common factor of .
Step 2.3.1.2.1.1
Cancel the common factor.
Step 2.3.1.2.1.2
Divide by .
Step 2.3.1.3
Simplify the right side.
Step 2.3.1.3.1
Divide by .
Step 2.3.2
Since the left side has an even power, it is always positive for all real numbers.
All real numbers
All real numbers
All real numbers
Step 3
The domain is all real numbers.
Interval Notation:
Set-Builder Notation:
Step 4