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# Precalculus Examples

Step 1

Set the radicand in greater than or equal to to find where the expression is defined.

Step 2

Step 2.1

Subtract from both sides of the inequality.

Step 2.2

Divide each term in by and simplify.

Step 2.2.1

Divide each term in by . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

Step 2.2.2

Simplify the left side.

Step 2.2.2.1

Dividing two negative values results in a positive value.

Step 2.2.2.2

Divide by .

Step 2.2.3

Simplify the right side.

Step 2.2.3.1

Divide by .

Step 2.3

Take the specified root of both sides of the inequality to eliminate the exponent on the left side.

Step 2.4

Simplify the left side.

Step 2.4.1

Pull terms out from under the radical.

Step 2.5

Write as a piecewise.

Step 2.5.1

To find the interval for the first piece, find where the inside of the absolute value is non-negative.

Step 2.5.2

In the piece where is non-negative, remove the absolute value.

Step 2.5.3

To find the interval for the second piece, find where the inside of the absolute value is negative.

Step 2.5.4

In the piece where is negative, remove the absolute value and multiply by .

Step 2.5.5

Write as a piecewise.

Step 2.6

Find the intersection of and .

Step 2.7

Solve when .

Step 2.7.1

Divide each term in by and simplify.

Step 2.7.1.1

Divide each term in by . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

Step 2.7.1.2

Simplify the left side.

Step 2.7.1.2.1

Dividing two negative values results in a positive value.

Step 2.7.1.2.2

Divide by .

Step 2.7.1.3

Simplify the right side.

Step 2.7.1.3.1

Move the negative one from the denominator of .

Step 2.7.1.3.2

Rewrite as .

Step 2.7.2

Find the intersection of and .

Step 2.8

Find the union of the solutions.

Step 3

The domain is all values of that make the expression defined.

Interval Notation:

Set-Builder Notation:

Step 4