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Trigonometry 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
Take the natural logarithm of both sides of the equation to remove the variable from the exponent.
Step 1.2.2
The equation cannot be solved because is undefined.
Undefined
Step 1.2.3
There is no solution for
No solution
No solution
Step 1.3
Set the denominator in equal to to find where the expression is undefined.
Step 1.4
Solve for .
Step 1.4.1
To remove the radical on the left side of the equation, square both sides of the equation.
Step 1.4.2
Simplify each side of the equation.
Step 1.4.2.1
Use to rewrite as .
Step 1.4.2.2
Simplify the left side.
Step 1.4.2.2.1
Multiply the exponents in .
Step 1.4.2.2.1.1
Apply the power rule and multiply exponents, .
Step 1.4.2.2.1.2
Cancel the common factor of .
Step 1.4.2.2.1.2.1
Cancel the common factor.
Step 1.4.2.2.1.2.2
Rewrite the expression.
Step 1.4.2.3
Simplify the right side.
Step 1.4.2.3.1
Raising to any positive power yields .
Step 1.4.3
Solve for .
Step 1.4.3.1
Take the natural logarithm of both sides of the equation to remove the variable from the exponent.
Step 1.4.3.2
The equation cannot be solved because is undefined.
Undefined
Step 1.4.3.3
There is no solution for
No solution
No solution
No solution
Step 1.5
The domain is all real numbers.
Interval Notation:
Set-Builder Notation:
Interval Notation:
Set-Builder Notation:
Step 2
Since the domain is all real numbers, is continuous over all real numbers.
Continuous
Step 3