Finite Math Examples

Find Where Undefined/Discontinuous square root of 2n^2-1
Step 1
Set the radicand in less than to find where the expression is undefined.
Step 2
Solve for .
Tap for more steps...
Step 2.1
Add to 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 .
Step 2.2.2
Simplify the left side.
Tap for more steps...
Step 2.2.2.1
Cancel the common factor of .
Tap for more steps...
Step 2.2.2.1.1
Cancel the common factor.
Step 2.2.2.1.2
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
Any root of is .
Step 2.4.2.1.3
Multiply by .
Step 2.4.2.1.4
Combine and simplify the denominator.
Tap for more steps...
Step 2.4.2.1.4.1
Multiply by .
Step 2.4.2.1.4.2
Raise to the power of .
Step 2.4.2.1.4.3
Raise to the power of .
Step 2.4.2.1.4.4
Use the power rule to combine exponents.
Step 2.4.2.1.4.5
Add and .
Step 2.4.2.1.4.6
Rewrite as .
Tap for more steps...
Step 2.4.2.1.4.6.1
Use to rewrite as .
Step 2.4.2.1.4.6.2
Apply the power rule and multiply exponents, .
Step 2.4.2.1.4.6.3
Combine and .
Step 2.4.2.1.4.6.4
Cancel the common factor of .
Tap for more steps...
Step 2.4.2.1.4.6.4.1
Cancel the common factor.
Step 2.4.2.1.4.6.4.2
Rewrite the expression.
Step 2.4.2.1.4.6.5
Evaluate the exponent.
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
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 equation is undefined where the denominator equals , the argument of a square root is less than , or the argument of a logarithm is less than or equal to .
Step 4
The result can be shown in multiple forms.
Inequality Form:
Interval Notation:
Step 5