Algebra Examples

$f (x) = x^{2}$ , $g (x) = x - 1$

Replace the function designators with the actual functions in $\frac{f (x)}{g (x)}$ .

$\frac{x^{2}}{x - 1}$

Set the denominator in $\frac{x^{2}}{x - 1}$ equal to $0$ to find where the expression is undefined.

$x - 1 = 0$

Add $1$ to both sides of the equation.

$x = 1$

The domain is all values of $x$ that make the expression defined.

Interval Notation:

$(- \infty, 1) \cup (1, \infty)$

Set-Builder Notation:

${x | x \neq 1}$

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