Algebra Examples

$f (x) = {\begin{cases} - x + 3 & x < 1 \\ 3 x - 1 & x \geq 1 \end{cases}$

Step 1

Since the domain of $- x + 3$ is all real numbers, the domain of this piece of the function is its restriction, $x < 1$ .

$(- \infty, 1)$

Step 2

Since the domain of $3 x - 1$ is all real numbers, the domain of this piece of the function is its restriction, $x \geq 1$ .

$[1, \infty)$

Step 3

Find the domain by taking the union of all of the intervals where the function is defined.

$(- \infty, \infty)$

Step 4