Identify any restrictions on the input variable (e.g., denominators not equal to 0, expressions under radicals nonnegative, logs arguments positive).
For rational functions, set each denominator equal to 0 and exclude those input values.
For square roots (and other even roots), set the radicand ≥ 0 and solve for the variable.
For logarithms, set the argument > 0 and solve for the variable.
For functions with inverse trig, ensure the input is within the required range (e.g., for arcsin/arccos: input between −1 and 1, inclusive).
For piecewise functions, determine the domain of each piece separately and then combine them.
If absolute values or polynomials are involved, include all real inputs unless another restriction applies.
Combine all allowed input values into one set using interval notation or set-builder notation.