Find the Domain f(x)=x^2 if x<=0; 1/x if x>0

$f (x) = {\begin{cases} x^{2} & x \leq 0 \\ \frac{1}{x} & x > 0 \end{cases}$

Step 1

Since the domain of $x^{2}$ is all real numbers, the domain of this piece of the function is its restriction, $x \leq 0$ .

$(- \infty, 0]$

Step 2

Find the domain for $\frac{1}{x}$ .

$(- \infty, 0) \cup (0, \infty)$

Step 3

Compare the domain of $\frac{1}{x}$ with the restriction $x > 0$ to see where this piece of the function is defined.

$(0, \infty)$

Step 4

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

$(- \infty, \infty)$

Step 5