Algebra Examples

$f (x) = {\begin{cases} x + 4 & - 4 \leq x < 3 \\ 2 x - 1 & 3 \leq x < 6 \end{cases}$

Step 1

Since the domain of $x + 4$ is all real numbers, the domain of this piece of the function is its restriction, $- 4 \leq x < 3$ .

$[- 4, 3)$

Step 2

Since the domain of $2 x - 1$ is all real numbers, the domain of this piece of the function is its restriction, $3 \leq x < 6$ .

$[3, 6)$

Step 3

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

$[- 4, 6)$

Step 4