Find the Domain f(x)=4x-4 if x<=1; x+2 if x>1

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

Step 1

Since the domain of $4 x - 4$ is all real numbers, the domain of this piece of the function is its restriction, $x \leq 1$ .

$(- \infty, 1]$

Step 2

Since the domain of $x + 2$ is all real numbers, the domain of this piece of the function is its restriction, $x > 1$ .

$(1, \infty)$

Step 3

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

$(- \infty, \infty)$

Step 4