Algebra Examples

f (x) = x^{2}

$f (x) = x^{2}$ ,

g (x) = x - 1

$g (x) = x - 1$

Step 1

Replace the function designators with the actual functions in

\frac{f (x)}{g (x)}

$\frac{f (x)}{g (x)}$ .

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

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

Step 2

Set the denominator in

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

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

0

$0$ to find where the expression is undefined.

x - 1 = 0

$x - 1 = 0$

Step 3

Add

1

$1$ to both sides of the equation.

x = 1

$x = 1$

Step 4

The domain is all values of

x

$x$ that make the expression defined.

Interval Notation:

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

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

Set-Builder Notation:

{x | x \neq 1}

${x | x \neq 1}$

Step 5

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