# Note that undefined variables are inserted in where

## How to find the domain of a function defined by an equation

Rewrite the equation and replace f (x) with y. This brings the equation into a standard form and makes it easier to use.

Examine your function. Using algebraic methods, move all variables with the same symbol to one side of the equation. Most of the time, you'll move all of your "x" to one side of the equation while keeping your "y" value on the other side of the equation.

Take the necessary steps to make "y" positive and alone. That means if you had "-y = -x + 2" you would multiply the whole equation by "-1" to make "y" positive. Also, if you had "2y = 2x + 4", you would divide the entire equation by 2 (or multiply by 1/2) to express it as "y = x + 2".

Determine which "x" values would satisfy the equation. It does this by first determining which values do not satisfy the equation. Simple equations like the one above can be satisfied with all "x" values, which means any number in the equation would work. However, for more complex equations with square roots and fractions, certain numbers do not satisfy the equation. This is because if these numbers were put into the equation, they would result in either imaginary numbers or undefined values that cannot be part of the domain. For example, in “y = 1 / x”, “x” cannot equal 0.

List the "x" values that satisfy the equation as a quantity, each number separated by commas and all numbers in square brackets, like this: {-1, 2, 5, 9}. It is common practice to list the values in numerical order, but this is not strictly necessary. In some cases you want to use inequalities to express the domain of the function. If you continue with the example from step 4, the domain is {x <0, x> 0}.

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