Start with all real numbers as the possible input values
Exclude values that make any denominator equal to zero
Exclude values that make any even root have a negative radicand
Exclude values that make any logarithm have a nonpositive argument
Exclude values that make inverse trigonometric inputs fall outside their allowed ranges
Apply any restrictions from piecewise definitions
Combine all restrictions to get the remaining valid input values
Write the domain in interval notation or set notation