Algebra Examples

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

Step 1

Find the domain for $\sqrt{x + 5}$ .

$[- 5, \infty)$

Step 2

Compare the domain of $\sqrt{x + 5}$ with the restriction $- 5 \leq x \leq - 1$ to see where this piece of the function is defined.

$[- 5, - 1]$

Step 3

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

$(- 1, \infty)$

Step 4

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

$[- 5, \infty)$

Step 5