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Pre-Algebra Examples
Step 1
Step 1.1
Set the radicand in greater than or equal to to find where the expression is defined.
Step 1.2
Solve for .
Step 1.2.1
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Step 1.2.2
Set equal to .
Step 1.2.3
Set equal to and solve for .
Step 1.2.3.1
Set equal to .
Step 1.2.3.2
Solve for .
Step 1.2.3.2.1
Take the natural logarithm of both sides of the equation to remove the variable from the exponent.
Step 1.2.3.2.2
The equation cannot be solved because is undefined.
Undefined
Step 1.2.3.2.3
There is no solution for
No solution
No solution
No solution
Step 1.2.4
The final solution is all the values that make true.
Step 1.2.5
The solution consists of all of the true intervals.
Step 1.3
The domain is all values of that make the expression defined.
Interval Notation:
Set-Builder Notation:
Interval Notation:
Set-Builder Notation:
Step 2
Step 2.1
Replace the variable with in the expression.
Step 2.2
Simplify the result.
Step 2.2.1
Multiply by .
Step 2.2.2
Rewrite as .
Step 2.2.3
Pull terms out from under the radical, assuming positive real numbers.
Step 2.2.4
The final answer is .
Step 3
The radical expression end point is .
Step 4
Step 4.1
Substitute the value into . In this case, the point is .
Step 4.1.1
Replace the variable with in the expression.
Step 4.1.2
Simplify the result.
Step 4.1.2.1
Multiply by .
Step 4.1.2.2
The final answer is .
Step 4.2
Substitute the value into . In this case, the point is .
Step 4.2.1
Replace the variable with in the expression.
Step 4.2.2
Simplify the result.
Step 4.2.2.1
Reorder and .
Step 4.2.2.2
Pull terms out from under the radical.
Step 4.2.2.3
The final answer is .
Step 4.3
The square root can be graphed using the points around the vertex
Step 5