Algebra Examples

Find the Domain and Range square root of 4-x^2
Step 1
Set the radicand in greater than or equal to to find where the expression is defined.
Step 2
Solve for .
Tap for more steps...
Step 2.1
Subtract from both sides of the inequality.
Step 2.2
Divide each term in by and simplify.
Tap for more steps...
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.
Tap for more steps...
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.
Tap for more steps...
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 equation.
Tap for more steps...
Step 2.4.1
Simplify the left side.
Tap for more steps...
Step 2.4.1.1
Pull terms out from under the radical.
Step 2.4.2
Simplify the right side.
Tap for more steps...
Step 2.4.2.1
Simplify .
Tap for more steps...
Step 2.4.2.1.1
Rewrite as .
Step 2.4.2.1.2
Pull terms out from under the radical.
Step 2.4.2.1.3
The absolute value is the distance between a number and zero. The distance between and is .
Step 2.5
Write as a piecewise.
Tap for more steps...
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 .
Tap for more steps...
Step 2.7.1
Divide each term in by and simplify.
Tap for more steps...
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.
Tap for more steps...
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.
Tap for more steps...
Step 2.7.1.3.1
Divide by .
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
The range is the set of all valid values. Use the graph to find the range.
Interval Notation:
Set-Builder Notation:
Step 5
Determine the domain and range.
Domain:
Range:
Step 6