Finite Math Examples

$f (x) = 3 x^{2}$ , $g (x) = x + 5$

Step 1

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

$\frac{3 x^{2}}{x + 5}$

Step 2

Set the denominator in $\frac{3 x^{2}}{x + 5}$ equal to $0$ to find where the expression is undefined.

$x + 5 = 0$

Step 3

Subtract $5$ from both sides of the equation.

$x = - 5$

Step 4

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

Interval Notation:

$(- \infty, - 5) \cup (- 5, \infty)$

Set-Builder Notation:

${x | x \neq - 5}$

Step 5