EDGE Math 8

Functions

Suppose that a function f is expressed as an equation, $y = f (x) .$ If the domain of f is not specified, it is understood that its domain will consist of all real numbers x such that the value of $f (x)$ is a real number.

Example

Find the domain of each function.

g (x) = x^{2} + x + 3

\frac{x}{x + 9}

\frac{1}{x^{2} - 9}

Solution

1. Notice that in $g (x) = x^{2} + x + 3,$ you can assign any real number to x. Thus, the domain of g is the set of all real numbers.

2. Recall that in a fraction, the denominator cannot be equal to zero. So, in

\frac{x}{x + 9},

x + 9

should not be equal to zero. Thus, x cannot be equal to –9. The domain of f is the set of all real numbers except

x = - 9.

In set notation, it is written as

{x | x \in ℝ and x \neq - 9} .

3. The denominator $x^{2} - 9$ should not be equal to zero. Hence, the value of x cannot be 3 or –3; that is, the domain is the set ${x | x \in ℝ, x \neq - 3, and x \neq 3} .$