How to Find the Domain of a Function Algebraically?

Set every denominator equal to zero and exclude those values

For even roots, set the radicand greater than or equal to zero

For logarithms, set the argument greater than zero

For inverse trigonometric functions, apply their required input restrictions

For rational expressions, exclude any values that make the denominator zero

For square roots in denominators, require the radicand to be greater than zero

For composite functions, combine all restrictions from each part

Solve the resulting inequalities or equations

Write the domain using interval notation or set notation

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