Plug a value into the function for x to determine whether it lies within the function's domain. For example, if you have the function "x / 4," you could plug in 8.
Solve the expression. In the example, 8 / 4 = 2.
Determine whether the value you plugged in would lead to a real number if you solved the equation. In the function "x / 4", the domain is the set of all real numbers. As another example, the domain of "x^2 / x - 4" is the set of all real numbers except for 4, which would lead to a denominator of 0. You also cannot have the square root of a negative number.