Finite Math Examples

$f (x) = x$ , $g (x) = x + 3$

Step 1

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

$\frac{x}{x + 3}$

Step 2

Set the denominator in $\frac{x}{x + 3}$ equal to $0$ to find where the expression is undefined.

$x + 3 = 0$

Step 3

Subtract $3$ from both sides of the equation.

$x = - 3$

Step 4

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

Interval Notation:

$(- \infty, - 3) \cup (- 3, \infty)$

Set-Builder Notation:

${x | x \neq - 3}$

Step 5