Algebra Examples

$f (x) = {\begin{cases} \sqrt{x + 1} & - 1 \leq x \leq 3 \\ 5 - x & x > 3 \end{cases}$

Step 1

Find the domain for $\sqrt{x + 1}$ .

$[- 1, \infty)$

Step 2

Compare the domain of $\sqrt{x + 1}$ with the restriction $- 1 \leq x \leq 3$ to see where this piece of the function is defined.

$[- 1, 3]$

Step 3

Since the domain of $5 - x$ is all real numbers, the domain of this piece of the function is its restriction, $x > 3$ .

$(3, \infty)$

Step 4

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

$[- 1, \infty)$

Step 5