Find the Domain f(x)=3 if x<=4; -2x if x>4

$f (x) = {\begin{cases} 3 & x \leq 4 \\ - 2 x & x > 4 \end{cases}$

Step 1

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

$(- \infty, 4]$

Step 2

Since the domain of $- 2 x$ is all real numbers, the domain of this piece of the function is its restriction, $x > 4$ .

$(4, \infty)$

Step 3

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

$(- \infty, \infty)$

Step 4