Domain Math Example 2

Follow the full solution, then compare it with the other examples linked below.

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Find the domain of

g(x) = \frac{1}{x^2 - 4}

1
The denominator cannot be zero: $x^2 - 4 \neq 0$ .
2
Factor: $(x - 2)(x + 2) \neq 0$ , so $x \neq 2$ and $x \neq -2$ .
3
The domain is all real numbers except $\pm 2$ : $(-\infty, -2) \cup (-2, 2) \cup (2, \infty)$ .

Answer

(-\infty, -2) \cup (-2, 2) \cup (2, \infty)

For rational functions, exclude values that make the denominator zero. Factor the denominator to find these excluded values.

About Domain

The domain of a function is the complete set of allowable input values for which the function produces a defined, valid output.

Find the domain of [formula].

Find the domain of [formula].

Find the domain of [formula].